Reflection of Light and Spherical Mirrors Questions in English

(N/A) Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

(B) Radius of curvature,$R = 20\, cm$.
The relationship between the radius of curvature $(R)$ and the focal length $(f)$ of a spherical mirror is given by the formula: $R = 2f$.
To find the focal length $(f)$,we rearrange the formula: $f = \frac{R}{2}$.
Substituting the given value: $f = \frac{20\, cm}{2} = 10\, cm$.
Therefore,the focal length of the given spherical mirror is $10\, cm$.

(A) concave mirror produces an erect and enlarged image when the object is placed between the pole $(P)$ and the principal focus $(F)$ of the mirror.
In this position,the light rays appear to diverge from behind the mirror,forming a virtual image that is larger than the actual object.

(B) Convex mirrors are preferred as rear-view mirrors in vehicles for the following reasons:
$1$. They always form a virtual,erect,and diminished image of the objects placed in front of them.
$2$. They have a wider field of view compared to plane mirrors,which allows the driver to see a larger area of the traffic behind the vehicle.
$3$. This helps the driver in safe driving by providing a better perspective of the vehicles approaching from the rear.

(A) The radius of curvature $(R)$ of the convex mirror is given as $32\, cm$.
The relationship between the radius of curvature $(R)$ and the focal length $(f)$ of a spherical mirror is given by the formula: $R = 2f$.
To find the focal length $(f)$,we rearrange the formula: $f = \frac{R}{2}$.
Substituting the given value: $f = \frac{32\, cm}{2} = 16\, cm$.
Therefore,the focal length of the given convex mirror is $16\, cm$.

(D) concave mirror forms a virtual,erect,and magnified image only when the object is placed between the pole $(P)$ and the principal focus $(F)$ of the mirror.
In this position,the light rays appear to diverge from behind the mirror,creating a virtual image that is larger than the object.

(N/A) The range of the object distance should be between $0\, cm$ and $15\, cm$ (i.e.,between the pole $P$ and the principal focus $F$).
$A$ concave mirror produces an erect image only when the object is placed between its pole $(P)$ and the principal focus $(F)$.
The nature of the image formed is virtual and erect.
The image is larger (magnified) than the object.
The ray diagram showing the image formation is provided in the image below.

(N/A) Concave mirror.
$A$ concave mirror is used in the headlights of a car. This is because when a light source (bulb) is placed at the principal focus of a concave mirror,the light rays after reflection travel as a powerful parallel beam of light,which helps in illuminating the road at a long distance.

(CONVEX) The type of mirror used is a $Convex$ mirror.
Reason:
$1$. $Convex$ mirrors always form a virtual,erect,and diminished image of the objects placed in front of them.
$2$. They have a wider field of view compared to plane or concave mirrors,which allows the driver to see a larger area of the traffic behind the vehicle.
$3$. This helps the driver in safe driving by providing a better view of the road conditions behind.

(CONCAVE MIRROR) Concave mirror.
Concave mirrors are converging mirrors. They are used in solar furnaces because they converge the parallel rays of sunlight incident on them to a single point,known as the principal focus. This concentration of light energy produces a large amount of heat at that point,which is useful for heating purposes.

(A) solar cooker uses the heat of sunlight to cook and heat food. $A$ mirror is used to reflect and focus sunlight at a single point. $A$ concave mirror is best suited for this purpose. The concave mirror converges all the incident parallel rays of sunlight at its focus. This concentration of light energy significantly increases the temperature at that point,which is used to cook or heat the food placed there.

(B) The rays from the Sun are parallel to the principal axis and converge at the focus $(F)$ of the concave mirror. Therefore,the focal length $(f)$ of the mirror is $15 \, cm$.
For a concave mirror,the image size is equal to the object size when the object is placed at the center of curvature $(C)$.
The center of curvature is at a distance equal to twice the focal length $(R = 2f)$.
Thus,$R = 2 \times 15 \, cm = 30 \, cm$.
Therefore,the object should be placed at $30 \, cm$ in front of the mirror.

(C) convex mirror is used to see a full-length image of a distant tall building because it always forms a virtual,erect,and diminished image of objects placed in front of it. Due to its outward-curved surface,it has a wider field of view,allowing it to capture the entire image of a large object within a small mirror area. Plane mirrors would require a mirror of at least half the height of the building to see the full image,which is impractical for a distant tall building.

(D) In torches,searchlights,and vehicle headlights,a concave mirror is used as a reflector.
According to the properties of a concave mirror,when a light source (bulb) is placed at the focus $(F)$,the light rays emanating from it strike the mirror and are reflected as a parallel beam of light.
This parallel beam of light travels over a long distance,which is essential for these devices to illuminate distant objects.
Therefore,the bulb is placed very near to the focus of the reflector.

(A) The laws of reflection state that:
$1$. The angle of incidence is equal to the angle of reflection $(i = r)$.
$2$. The incident ray,the reflected ray,and the normal to the mirror surface at the point of incidence all lie in the same plane.
These laws are universal and apply to all types of reflecting surfaces,including plane mirrors,concave mirrors,and convex mirrors,regardless of their shape or curvature.

(D) According to the rules of reflection for a concave mirror,a ray of light parallel to the principal axis,after reflection,passes through the principal focus $(F)$ of the mirror.
In the given figure,the incident ray is parallel to the principal axis.
Therefore,after reflection,it must pass through the principal focus $(F)$.
Looking at the options,option $D$ correctly shows the reflected ray passing through the principal focus $(F)$.
Thus,the correct ray diagram is $D$.

(B) $1$. $A$ concave mirror produces a magnified image when the object is placed close to it. Since the head appears bigger, the top part of the mirror is concave.
$2$. $A$ plane mirror produces an image of the same size as the object. Since the middle portion appears of the same size, the middle part of the mirror is plane.
$3$. $A$ convex mirror always produces a diminished (smaller) image. Since the legs appear smaller, the bottom part of the mirror is convex.
$4$. Therefore, the order of the mirrors from top to bottom is concave, plane, and convex.

(N/A) When two plane mirrors are placed at an angle of $90^{\circ}$ to each other,the incident ray and the final reflected ray will always be parallel to each other,regardless of the angle of incidence.
Explanation:
$1$. Let the two mirrors be $M_1$ and $M_2$ placed at $90^{\circ}$.
$2$. The incident ray strikes $M_1$ at an angle of incidence $i$. According to the law of reflection,the angle of reflection $r = i$.
$3$. The reflected ray from $M_1$ acts as the incident ray for $M_2$. By geometry,the angle of incidence at $M_2$ will be $(90^{\circ} - i)$.
$4$. The final angle of reflection at $M_2$ will also be $(90^{\circ} - i)$.
$5$. By calculating the total deviation or the angles with the normal,it can be shown that the final reflected ray is parallel to the initial incident ray.

(N/A) To draw the ray diagrams for a concave mirror,follow these steps for each case:
$(a)$ Between $P$ and $F$: The image is virtual,erect,and magnified,formed behind the mirror.
$(b)$ Between $F$ and $C$: The image is real,inverted,and magnified,formed beyond $C$.
$(c)$ At $C$: The image is real,inverted,and of the same size as the object,formed at $C$.
$(d)$ Beyond $C$: The image is real,inverted,and diminished,formed between $F$ and $C$.
$(e)$ At infinity: The image is real,inverted,and highly diminished (point-sized),formed at the focus $F$.

(N/A) For a convex mirror:
$(a)$ When the object is at infinity,the incident rays are parallel to the principal axis. After reflection,they appear to diverge from the principal focus $(F)$ behind the mirror. The image formed is virtual,erect,highly diminished,and located at the principal focus $(F)$ behind the mirror.
$(b)$ When the object is at a finite distance from the mirror,the image formed is always virtual,erect,and diminished. It is located between the pole $(P)$ and the principal focus $(F)$ behind the mirror,regardless of the object's distance.

(N/A) The phenomenon of bouncing back of light rays when they strike a smooth or polished surface is known as reflection of light. When light hits a surface,it changes its direction and returns to the same medium.

(N/A) $(i)$ Angle of incidence: It is the angle between the incident ray and the normal at the point of incidence.
$(ii)$ Angle of reflection: It is the angle between the reflected ray and the normal at the point of incidence.
$(iii)$ Plane of incidence: It is the plane that contains the incident ray,the reflected ray,and the normal at the point of incidence.

(N/A) $(i)$ The angle of incidence $(i)$ is equal to the angle of reflection $(r)$,i.e.,$i = r$.
$(ii)$ The incident ray,the normal to the mirror at the point of incidence,and the reflected ray all lie in the same plane.

(B) The image formed by a plane mirror undergoes lateral inversion,which means the left side of the object appears as the right side in the image.
When a driver looks into their rear-view mirror,they see the word $AMBULANCE$ written in reverse on the vehicle behind them.
Due to the lateral inversion caused by the rear-view mirror,the word appears correctly oriented to the driver.
This allows the driver to quickly identify the vehicle as an $AMBULANCE$ and give way.

(B) plane mirror always forms a virtual and erect image.
The size of the image is equal to the size of the object (unmagnified).
The image formed is laterally inverted,meaning it exhibits right-left reversal.
Therefore,the image is virtual,erect,and of the same size as the object.

(A) Yes,a plane mirror can be considered a spherical mirror with an infinite radius of curvature $(R = \infty)$.
Since the focal length $(f)$ is half of the radius of curvature $(f = R/2)$,the focal length of a plane mirror is also infinite $(f = \infty)$.

(B) plane mirror can be considered as a part of a spherical mirror with an infinitely large radius of curvature. Since the surface of a plane mirror is perfectly flat,it does not curve at any point. Mathematically,the radius of curvature $(R)$ is related to the focal length $(f)$ by the formula $R = 2f$. For a plane mirror,the focal length is considered to be infinity,therefore the radius of curvature is also infinity.

(C) When two plane mirrors are placed parallel to each other,the light rays reflect back and forth between the two mirrors repeatedly. Each reflection creates a new image of the previous image. Since the mirrors are parallel,the angle between them is $0^{\circ}$. The formula for the number of images formed is $n = (360^{\circ} / \theta) - 1$. Substituting $\theta = 0^{\circ}$,we get $n = (360^{\circ} / 0^{\circ}) - 1$,which approaches infinity. Therefore,an infinite number of images are formed.

(A) When a ray of light is incident normally (perpendicularly) on a plane mirror,it strikes the surface along the normal.
By definition,the angle of incidence $(i)$ is the angle between the incident ray and the normal at the point of incidence.
Since the ray is incident along the normal,the angle between them is $0^{\circ}$,so $i = 0^{\circ}$.
According to the laws of reflection,the angle of incidence is equal to the angle of reflection $(i = r)$.
Therefore,the angle of reflection $(r)$ is also $0^{\circ}$.

(N/A) $(i)$ The image is of the same size as the object (unmagnified).
(ii) The image is virtual,meaning it cannot be caught on a screen.
(iii) The image is erect (upright).
(iv) The image exhibits lateral inversion (right-left reversal).

(N/A) spherical mirror is a mirror whose reflecting surface is a part of a hollow sphere of glass.
There are two main types of spherical mirrors:
$1$. Concave mirror: $A$ spherical mirror whose reflecting surface is curved inwards,i.e.,faces towards the center of the sphere.
$2$. Convex mirror: $A$ spherical mirror whose reflecting surface is curved outwards,i.e.,faces away from the center of the sphere.

(N/A) $(i)$ Pole (Vertex): The central point of the reflecting surface of a spherical mirror is called its pole.
$(ii)$ Centre of curvature: The centre of the sphere of which the mirror is a part is called the centre of curvature.
$(iii)$ Radius of curvature: The radius of the sphere of which the mirror is a part is called the radius of curvature.
$(iv)$ Principal axis: The straight line passing through the pole and the centre of curvature of the mirror is called the principal axis.
$(v)$ Principal focus: It is a point on the principal axis where light rays parallel to the principal axis converge or appear to diverge after reflection.
$(vi)$ Aperture: The effective diameter of the light-reflecting area of the spherical mirror is called its aperture.
$(vii)$ Focal length: The distance between the pole and the principal focus of a spherical mirror is called the focal length,represented by $f$.

(N/A) The principal focus of a convex mirror is a point on its principal axis. When rays of light parallel to the principal axis strike the convex mirror,they diverge after reflection. If these reflected rays are extended backwards,they appear to meet at this specific point on the principal axis. This point is known as the principal focus of the convex mirror.

(B) The focal length $(f)$ of a spherical mirror is related to its radius of curvature $(R)$ by the formula $f = R/2$.
For a plane mirror, the surface is flat, which means it can be considered as a part of a sphere with an infinite radius of curvature $(R = \infty)$.
Substituting this into the formula, we get $f = \infty / 2 = \infty$.
Therefore, the focal length of a plane mirror is infinity.

(N/A) $(i)$ Real image: When the rays of light,after reflection from a mirror,actually meet at a point,the image formed by these rays is called a real image. Real images can be obtained on a screen.
$(ii)$ Virtual image: When the rays of light,after reflection from a mirror,appear to meet at a point,the image formed by these rays is called a virtual image. Virtual images cannot be obtained on a screen.

(A) The relationship between the focal length $(f)$ and the radius of curvature $(R)$ of a spherical mirror is given by the formula $f = R / 2$.
Given that the radius of curvature $R = 36\, cm$.
Substituting the value into the formula: $f = 36\, cm / 2 = 18\, cm$.
Therefore,the focal length of the concave mirror is $18\, cm$.

(A) concave mirror is capable of forming a real image when the object is placed at a distance greater than the focal length $(f)$ of the mirror.
In contrast,a convex mirror and a plane mirror always form virtual and erect images for real objects.

(C) For a concave mirror,when an object is placed at the centre of curvature $(C)$,the light rays originating from the object reflect off the mirror and converge at the same point $(C)$.
This results in the formation of a real,inverted image that is exactly the same size as the object.
Therefore,the object is placed at the centre of curvature $(C)$.

(A) ray of light passing through the centre of curvature $(C)$ of a spherical mirror strikes the mirror surface normally (at an angle of $90^{\circ}$ to the tangent at the point of incidence).
According to the laws of reflection,when a ray strikes a surface normally,the angle of incidence $(i)$ is $0^{\circ}$.
Therefore,the angle of reflection $(r)$ is also $0^{\circ}$.
As a result,the ray reflects back along the same path,i.e.,$BCA$.

(N/A) To see an enlarged image of your face, you should use a $Concave$ mirror.
The face must be placed between the pole $(P)$ and the principal focus $(F)$ of the mirror.
When an object is placed between the pole and the focus of a $Concave$ mirror, the image formed is virtual, erect, and magnified (enlarged).

(C) concave mirror forms a real and diminished image when the object is placed beyond the centre of curvature $(C)$.
When the object is placed beyond $C$,the image is formed between the focus $(F)$ and the centre of curvature $(C)$.
The image formed is real,inverted,and diminished in size.

(B) convex mirror is a spherical mirror whose reflecting surface is curved outwards.
Due to its shape,it always forms a virtual,diminished,and erect image of objects placed in front of it.
Because the image formed is smaller than the object,a convex mirror can cover a much wider area than a plane or concave mirror.
Therefore,it provides a large field of view,which is why it is commonly used as a rear-view mirror in vehicles.

(A) Dentists use a concave mirror to examine teeth because it can produce an enlarged and virtual image of the object when the object is placed between the pole and the focus of the mirror. This helps in getting a clearer view of the tooth cavity or decay.

(A) $(i)$ Applications of concave mirror:
$1$. They are used as shaving mirrors to see a larger image of the face.
$2$. They are used by dentists to see enlarged images of teeth.
$3$. They are used as reflectors in torches,searchlights,and vehicle headlights to get powerful parallel beams of light.
$(ii)$ Applications of convex mirror:
$1$. They are used as rear-view mirrors in vehicles because they always give an erect,diminished image and have a wider field of view.
$2$. They are used as reflectors in streetlights to diverge light over a larger area.

(B) Drivers prefer convex mirrors as rearview mirrors because they always form a virtual,erect,and diminished image of the objects placed in front of them.
Due to the diminished size of the image,a convex mirror covers a much wider field of view compared to a plane mirror of the same size.
This allows the driver to see a larger area of the traffic behind the vehicle,which significantly enhances safety while driving.

(N/A) The diagram illustrates the key components of spherical mirrors:
$1$. Principal axis: The straight line passing through the pole and the centre of curvature of a spherical mirror.
$2$. Pole $(P)$: The centre of the reflecting surface of a spherical mirror.
$3$. Focus $(F)$: The point on the principal axis where light rays parallel to the principal axis converge (in a concave mirror) or appear to diverge (in a convex mirror) after reflection.
$4$. Centre of curvature $(C)$: The centre of the sphere of which the reflecting surface of the spherical mirror forms a part.
$5$. Radius of curvature $(R)$: The radius of the sphere of which the reflecting surface of the spherical mirror forms a part. It is the distance between the pole $(P)$ and the centre of curvature $(C)$.

(N/A) Advantage: $A$ convex mirror provides a wider field of view compared to a plane mirror,allowing the driver to see a larger area of the traffic behind.
Disadvantage: It does not show the correct distance of the vehicle at the rear; objects appear smaller and farther away than they actually are.

(N/A) According to the New Cartesian Sign Convention for spherical mirrors:
$1$. The object is always placed to the left of the mirror,so light travels from left to right.
$2$. All distances parallel to the principal axis are measured from the pole $(P)$ of the mirror.
$3$. Distances measured in the direction of incident light are taken as positive $(+)$.
$4$. Distances measured opposite to the direction of incident light are taken as negative $(-)$.
$5$. Distances measured perpendicular to and above the principal axis are taken as positive $(+)$.
$6$. Distances measured perpendicular to and below the principal axis are taken as negative $(-)$.

(N/A) According to the Cartesian sign convention for spherical mirrors and lenses:
$1$. All distances measured perpendicular to the principal axis and in the upward direction (above the principal axis) are taken as positive (+).
$2$. All distances measured perpendicular to the principal axis and in the downward direction (below the principal axis) are taken as negative (-).

(C) When an object is placed between the pole $(P)$ and the focus $(F)$ of a concave mirror,the light rays diverge after reflection.
These rays appear to meet behind the mirror when extended backwards.
Therefore,the image formed is virtual,erect,and magnified,and it is located behind the mirror.