Reflection of Light and Spherical Mirrors Questions in English

(A) convex mirror is a spherical mirror with its reflecting surface curved outwards.
Due to the nature of its curvature,light rays diverging from an object appear to meet behind the mirror after reflection.
Consequently,for any position of the object in front of a convex mirror,the image formed is always virtual,erect,and diminished in size.
Therefore,the statement is True.

(A) When a small lamp (point source of light) is placed at the principal focus $(F)$ of a concave mirror,the light rays originating from the lamp strike the mirror and are reflected parallel to the principal axis. This property is widely used in torches,searchlights,and vehicle headlights to produce a strong,parallel beam of light.

(B) plane mirror always forms a virtual,erect,and laterally inverted image of an object.
Since the reflected rays never actually meet at a point but only appear to diverge from a point behind the mirror,the image formed is always virtual.
Therefore,a plane mirror cannot form a real image.

(A) concave mirror can form a virtual,magnified,and erect image when the object is placed between the pole $(P)$ and the focus $(F)$ of the mirror. In this position,the light rays appear to diverge from behind the mirror,resulting in a virtual image that is larger than the object and upright.

(B) The statement is False. According to the laws of reflection,when a plane mirror is rotated by an angle $\theta$ while keeping the incident ray fixed,the reflected ray rotates by an angle $2\theta$ in the same direction. Since the original statement claims the reflected ray turns by an angle $\theta$,it is incorrect.

(A) In a plane mirror,the image formed is virtual,erect,and of the same size as the object. One of the fundamental properties of a plane mirror is that the object distance $(u)$ is equal to the image distance $(v)$ from the mirror surface. Therefore,the distance between the image and the mirror is exactly the same as the distance between the object and the mirror.

(B) The number of images $n$ formed by two plane mirrors inclined at an angle $\theta$ is given by the formula $n = (360^{\circ} / \theta) - 1$.
Given $\theta = 45^{\circ}$.
$n = (360^{\circ} / 45^{\circ}) - 1 = 8 - 1 = 7$.
Since the calculated number of images is $7$ and not $9$,the statement is False.

(A) When light reflects off a surface,it remains in the same medium. The properties of light such as frequency,wavelength,and speed depend on the nature of the medium. Since the medium does not change during reflection,these properties remain constant. Therefore,the statement is True.

(A) The statement is True.
Solar heating devices,such as solar cookers,often use concave (spherical) reflectors to focus parallel rays of sunlight onto a single point (the focus).
By concentrating the solar energy onto a small area,the intensity of heat increases significantly,allowing for the attainment of high temperatures required for cooking or heating purposes.

(C) For a spherical mirror of small aperture,the radius of curvature $(R)$ is twice the focal length $(f)$.
This relationship is expressed as $R = 2f$ or $f = R / 2$.
This is because the principal focus lies exactly at the midpoint between the pole and the center of curvature of the mirror.

(B) The surface of a book is rough and uneven at the microscopic level.
When light rays fall on such a rough surface,they are reflected in various directions.
This type of reflection is known as irregular or diffused reflection.
Regular reflection occurs only on smooth,polished surfaces like mirrors.

(B) When a light ray is directed towards the centre of curvature $(C)$ of a concave mirror,it 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,a ray incident normally on a spherical mirror reflects back along the same path.
Therefore,the reflected ray passes back through the centre of curvature $(C)$.

(C) concave mirror produces a virtual and erect image only when the object is placed between the pole $(P)$ and the principal focus $(F)$.
In this position,the light rays appear to diverge from behind the mirror,forming an enlarged,virtual,and erect image.
For all other positions (at $F$,between $F$ and $C$,at $C$,and beyond $C$),the image formed by a concave mirror is real and inverted.

(B) plane mirror can be considered as a spherical mirror with an infinite radius of curvature $(R = \infty)$.
Since the focal length $(f)$ is half of the radius of curvature $(f = R/2)$,it follows that $f = \infty / 2 = \infty$.
Therefore,the focal length of a plane mirror is infinity.

(A) In a plane mirror,the distance of the object from the mirror is equal to the distance of the image from the mirror.
Given that the object is at a distance of $2 \, m$ from the mirror.
Therefore,the image is also formed at a distance of $2 \, m$ behind the mirror.
The total distance between the object and its image is the sum of the distance of the object from the mirror and the distance of the image from the mirror.
Total distance = $2 \, m + 2 \, m = 4 \, m$.

(C) plane mirror always forms a virtual and erect image.
In a plane mirror,the image formed is of the same size as the object and is laterally inverted.
Since the light rays do not actually meet at the image point but appear to diverge from it,the image is virtual.
Therefore,the correct option is $C$.

(A) Light travels in a straight line,a phenomenon known as rectilinear propagation of light. This occurs because the wavelength of visible light is extremely small compared to the size of the objects it interacts with. Due to this very small wavelength,the diffraction effects are negligible in everyday life,causing light to appear to travel in a straight path.

(C) When light rays from an object strike the surface of a plane mirror,they bounce back into the same medium. This phenomenon of light bouncing back from a surface is known as reflection. $A$ plane mirror forms a virtual and erect image of an object due to the regular reflection of light.

(A) real image is formed when light rays actually intersect after reflection or refraction.
Because the light rays physically meet at the point of image formation,a real image can be captured or projected onto a screen.
Real images are always inverted relative to the object.
Therefore,the statement 'It can be obtained on a screen' is correct.

(A) For a plane mirror,the distance of the object from the mirror is equal to the distance of the image from the mirror.
Given that the object distance $(u)$ is $10 \ cm$.
According to the properties of a plane mirror,the image distance $(v)$ is equal to the object distance in magnitude.
Therefore,the image will be formed at a distance of $10 \ cm$ behind the mirror.

(D) plane mirror always forms an image that is virtual,erect,and of the same size as the object.
Since the light rays do not actually meet at the image point,the image is virtual.
Therefore,the correct statement is that the image formed is virtual.

(C) According to the laws of reflection,the angle of incidence $(i)$ is always equal to the angle of reflection $(r)$.
Given that the angle of incidence $(i)$ = $30^{\circ}$.
Therefore,the angle of reflection $(r)$ = $30^{\circ}$.

(C) The centre of the reflecting surface of a spherical mirror is a point called the pole. It lies on the surface of the mirror. It is usually represented by the letter $P$.

(D) When light rays parallel to the principal axis strike a spherical mirror,they reflect and converge at (or appear to diverge from) a specific point on the principal axis.
This point is known as the principal focus,denoted by the letter $F$.
For a concave mirror,the rays actually meet at this point,while for a convex mirror,they appear to diverge from this point.

(B) The distance between the pole $(P)$ and the principal focus $(F)$ of a spherical mirror is defined as the focal length $(f)$.
It is half of the radius of curvature $(R)$,represented by the relation $f = R/2$.

(C) spherical mirror is a part of a sphere. The center of the sphere of which the mirror is a part is called the $Centre of curvature$ $(C)$. The pole $(P)$ is the center of the reflecting surface of the mirror. The principal focus $(F)$ is a point on the principal axis where light rays parallel to the axis converge or appear to diverge. The principal axis is the line passing through the pole and the center of curvature. However,in the context of defining the geometric origin of the mirror,the $Centre of curvature$ is the fundamental point that defines the sphere from which the mirror is cut.

(C) When light rays parallel to the principal axis fall on a spherical mirror,they reflect and converge at (or appear to diverge from) a specific point on the principal axis.
This specific point is known as the Principal focus,denoted by the letter $F$.
For a concave mirror,the rays actually meet at this point,while for a convex mirror,they appear to diverge from this point.

(A) According to the rules of image formation by spherical mirrors,a ray of light passing through the principal focus $(F)$ of a concave mirror becomes parallel to the principal axis after reflection.
This is the converse of the rule where a ray parallel to the principal axis passes through the focus after reflection.

(A) For a concave mirror,when an object is placed beyond the centre of curvature $(C)$,the light rays from the object form a real,inverted,and diminished image between the focus $(F)$ and the centre of curvature $(C)$.
Therefore,the correct position for the object is beyond the centre of curvature.

(B) When an object is placed beyond the center of curvature $(C)$ of a concave mirror,the light rays from the object reflect off the mirror and converge between the center of curvature $(C)$ and the principal focus $(F)$.
Since the reflected rays actually meet at a point,the image formed is real.
Because the image is formed between $C$ and $F$,it is smaller in size than the object,i.e.,diminished.
Therefore,the image is real and diminished.

(A) For a concave mirror,when an object is placed beyond the center of curvature $(C)$,the image formed is real,inverted,and diminished.
$1$. The rays of light coming from the object pass through the mirror and converge between the principal focus $(F)$ and the center of curvature $(C)$.
$2$. Since the rays actually intersect,the image is real.
$3$. The size of the image is smaller than the object,hence it is diminished.

(D) When an object is placed at the center of curvature $(C)$ of a concave mirror,the light rays originating from the object follow the laws of reflection.
One ray passes parallel to the principal axis and reflects through the focus $(F)$.
Another ray passes through the focus $(F)$ and reflects parallel to the principal axis.
These reflected rays intersect exactly at the center of curvature $(C)$.
Therefore,the image formed is real,inverted,and of the same size as the object.

(A) For a concave mirror,when an object is placed at the center of curvature $(C)$,the light rays originating from the object strike the mirror and reflect back through the same path.
As a result,the image is formed at the center of curvature $(C)$ itself.
The image formed is real,inverted,and of the same size as the object.

(B) When an object is placed between the principal focus $(F)$ and the center of curvature $(C)$ of a concave mirror,the light rays from the object follow the rules of reflection:
$1$. $A$ ray parallel to the principal axis passes through the principal focus $(F)$ after reflection.
$2$. $A$ ray passing through the principal focus $(F)$ becomes parallel to the principal axis after reflection.
These reflected rays meet at a point beyond the center of curvature $(C)$.
Therefore,the image formed is real,inverted,and magnified,and it is located beyond the center of curvature $(C)$.

(D) For a concave mirror,when an object is placed between the principal focus $(F)$ and the center of curvature $(C)$:
$1$. The light rays from the object diverge and meet at a point beyond the center of curvature $(C)$.
$2$. The image formed is real because the light rays actually intersect.
$3$. The image is inverted.
$4$. The size of the image is larger than the object (magnified).
Therefore,the image formed is real and magnified.

(B) For a concave mirror,when an object is placed between the principal focus $(F)$ and the center of curvature $(C)$,the image formed is real,inverted,and magnified.
$1$. When the object is beyond $C$,the image is diminished,real,and inverted.
$2$. When the object is at $C$,the image is of the same size,real,and inverted.
$3$. When the object is between $F$ and $C$,the image is formed beyond $C$ and is magnified,real,and inverted.
$4$. When the object is between $F$ and the pole $(P)$,the image is virtual,erect,and magnified.

(B) When an object is placed between the principal focus $(F)$ and the pole $(P)$ of a concave mirror,the light rays diverge after reflection.
By extending these rays backward,they appear to meet behind the mirror.
Therefore,the image formed is virtual,erect,and magnified (larger than the object).
This is the only case where a concave mirror produces a virtual image.

(B) When an object is placed at the centre of curvature $(C)$ of a concave mirror,the light rays originating from the object follow the laws of reflection.
$1$. $A$ ray parallel to the principal axis passes through the principal focus $(F)$ after reflection.
$2$. $A$ ray passing through the principal focus $(F)$ emerges parallel to the principal axis after reflection.
These two reflected rays intersect exactly at the centre of curvature $(C)$.
Therefore,the image formed is real,inverted,and of the same size as the object,located at the centre of curvature $(C)$.

(A) convex mirror always forms a virtual,erect,and diminished image for any position of the object in front of it.
When an object is placed at any finite distance (including $2f$) in front of a convex mirror,the light rays diverge after reflection.
These rays appear to originate from a point behind the mirror.
The image is always formed between the pole $(P)$ and the principal focus $(F)$ behind the mirror.
Therefore,the correct option is $A$.

(D) concave mirror can form various types of images depending on the position of the object:
$1$. When the object is placed between the pole $(P)$ and the focus $(F)$,the image formed is virtual,erect,and enlarged.
$2$. When the object is placed at the focus $(F)$,the image is real,inverted,and highly enlarged.
$3$. When the object is placed between $F$ and $C$,the image is real,inverted,and enlarged.
$4$. When the object is placed at $C$,the image is real,inverted,and of the same size.
$5$. When the object is placed beyond $C$,the image is real,inverted,and diminished.
$6$. $A$ concave mirror can never form a virtual and diminished image. $A$ virtual and diminished image is only formed by a convex mirror.

(D) concave mirror can form both real and virtual images.
$1$. Real images: These can be enlarged (when the object is between $F$ and $C$),diminished (when the object is beyond $C$),or of the same size (when the object is at $C$).
$2$. Virtual images: $A$ concave mirror forms a virtual image only when the object is placed between the pole $(P)$ and the focus $(F)$. In this case,the image formed is always virtual,erect,and enlarged.
$3$. Therefore,a concave mirror can never form a virtual and diminished image. $A$ virtual and diminished image is only formed by a convex mirror.

(B) For a spherical mirror,the relationship between the focal length $(f)$ and the radius of curvature $(R)$ is given by the formula: $R = 2f$.
Given that the focal length $f = 20 \ cm$.
Substituting the value into the formula: $R = 2 \times 20 \ cm = 40 \ cm$.
Therefore,the radius of curvature is $40 \ cm$.

(A) The relationship between the focal length $(f)$ and the radius of curvature $(R)$ of a spherical mirror is given by the formula: $f = \frac{R}{2}$.
Given that the radius of curvature $R = 30 \ cm$.
Substituting the value of $R$ into the formula: $f = \frac{30 \ cm}{2} = 15 \ cm$.
Therefore,the focal length of the spherical mirror is $15 \ cm$.

(B) For a spherical mirror,the relationship between the radius of curvature $(R)$ and the focal length $(f)$ is given by $R = 2f$.
The principal focus $(F)$ lies exactly at the midpoint between the pole $(P)$ and the center of curvature $(C)$.
Therefore,the distance between the principal focus $(F)$ and the center of curvature $(C)$ is equal to the focal length $(f)$.

(C) For a concave mirror,a virtual and magnified image is formed only when the object is placed between the pole $(P)$ and the principal focus $(F)$.
This means the object distance $(u)$ must be less than the focal length $(f)$,i.e.,$u < f$.

(A) The magnification $(m)$ of a mirror is defined as the ratio of the image distance $(v)$ to the object distance $(u)$,given by $m = -v/u$.
For a magnified image,the absolute value of magnification must be greater than $1$,i.e.,$|m| > 1$.
This implies $|-v/u| > 1$,which simplifies to $|v| > |u|$.
In the context of a concave mirror,when the object is placed between the focus $(F)$ and the pole $(P)$,or between the focus $(F)$ and the center of curvature $(C)$,the image formed is magnified,meaning the image distance $(v)$ is greater than the object distance $(u)$.

(C) In a searchlight or torch,a concave mirror is used as a reflector.
According to the properties of a concave mirror,when a light source is placed at the principal focus $(F)$,the light rays originating from it strike the mirror and are reflected as a parallel beam of light.
These parallel rays do not diverge significantly and can travel over a long distance.
Therefore,the bulb is placed at the principal focus.