Spherical Lenses, Lens Formula and Power Questions in English

(B) When an object is placed at $2F_1$ in front of a convex lens,the light rays originating from the object pass through the lens and converge at $2F_2$ on the other side.
According to the rules of image formation by a convex lens,when the object distance $u = 2F$,the image distance $v = 2F$.
The image formed is real,inverted,and of the same size as the object.

(C) When an object is placed between the principal focus $(F)$ and the optical center $(O)$ of a convex lens,the light rays diverge after refraction.
By extending these rays backward,they appear to meet behind the object on the same side of the lens.
Therefore,the image formed is virtual,erect,and magnified (larger than the object).
This property is used in simple microscopes or magnifying glasses.

(D) When an object is placed at the principal focus $(F)$ of a convex lens,the light rays coming from the object pass through the lens and become parallel to the principal axis.
These parallel rays do not meet on the same side of the lens and appear to meet at infinity.
Therefore,the image is formed at infinity,is real,inverted,and highly enlarged.

(B) For a convex lens,when an object is placed at $2F$ (twice the focal length),the light rays pass through the lens and converge at $2F$ on the other side.
This results in an image that is real,inverted,and exactly the same size as the object.
Therefore,the correct position is at $2F$.

(C) ray of light passing through the optical center $(O)$ of a thin lens goes straight without any deviation or refraction.
This happens because the optical center is the central point of the lens where the incident ray strikes the surface at an angle of $90^{\circ}$ (normal incidence),resulting in no bending of the light path.

(A) For a convex lens,when an object is placed between the optical center $(O)$ and the principal focus $(F)$,the light rays diverge after refraction.
When these rays are traced backward,they appear to meet at a point on the same side of the lens as the object.
This results in the formation of a virtual,erect,and magnified image on the same side as the object.
Therefore,the correct position is between the principal focus and the optical center.

(D) convex lens can form real images (when the object is placed beyond the focus) which can be either magnified,diminished,or the same size as the object.
It can also form a virtual and magnified image when the object is placed between the optical center and the focus.
However,a convex lens cannot form a virtual and diminished image. $A$ virtual and diminished image is only formed by a concave lens or a convex mirror.

(B) concave lens is a diverging lens.
For any position of an object placed in front of a concave lens,the light rays diverge after refraction.
When these rays are extended backward,they appear to meet at a point on the same side of the lens as the object.
Therefore,the image formed is always virtual,erect,and diminished in size,regardless of the object's distance from the lens.

(A) concave lens is a diverging lens. Regardless of the position of the object (placed anywhere between the optical center and infinity),the light rays diverge after refraction. When these rays are extended backward,they appear to meet between the optical center $(O)$ and the principal focus $(F_1)$ on the same side as the object. The image formed is always virtual,erect,and diminished.

(B) lens is typically formed by the intersection of two spherical surfaces.
Each of these spherical surfaces forms a part of a sphere.
The centre of each such sphere is called the centre of curvature of the lens.
Since a lens has two spherical surfaces,it has two centres of curvature,usually represented as $C_1$ and $C_2$.

(C) convex mirror always forms a virtual,erect,and diminished image for any position of the object in front of it.
Similarly,a concave lens always forms a virtual,erect,and diminished image for any position of the object in front of it.
Therefore,both convex mirrors and concave lenses are characterized by their ability to always produce virtual images regardless of the object's distance.

(B) The lens formula relates the focal length $(f)$,the object distance $(u)$,and the image distance $(v)$ for a spherical lens.
It is given by the expression: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$.
Here,$v$ is the distance of the image from the optical center,$u$ is the distance of the object from the optical center,and $f$ is the focal length of the lens.

(A) dioptre meter (also known as a lensmeter or focimeter) is an ophthalmic instrument used to measure the refractive power of a lens.
Since the power of a lens $(P)$ is defined as the reciprocal of its focal length $(f)$ in meters $(P = 1/f)$,the instrument directly measures the dioptric power of spectacle lenses.

(A) The power $(P)$ of a lens is defined as the reciprocal of its focal length $(f)$ in meters.
Formula: $P = \frac{1}{f(m)}$.
Given: Focal length $(f)$ = $50 \ cm = 0.5 \ m$.
Since it is a convex lens,the focal length is positive $(f = +0.5 \ m)$.
Calculation: $P = \frac{1}{+0.5 \ m} = +2.0 \ D$.
Therefore,the power of the convex lens is $+2.0 \ D$.

(A) The power $(P)$ of a lens is defined as the reciprocal of its focal length $(f)$ in meters.
Formula: $P = \frac{1}{f(m)}$.
Given: Power $(P)$ = $+2.0 \ D$.
Substituting the value in the formula: $2.0 = \frac{1}{f}$.
Therefore,$f = \frac{1}{2.0} = 0.5 \ m$.
Since the power is positive,the lens is a convex lens,and the focal length is positive $(+0.5 \ m)$.

(C) The focal length $(f)$ of the convex lens is given as $20 \text{ cm}$.
Since the focal length must be in meters for the power calculation,we convert it: $f = 20 \text{ cm} = 0.2 \text{ m}$.
The formula for the power $(P)$ of a lens is $P = 1/f$ (where $f$ is in meters).
Substituting the value: $P = 1 / 0.2 = 5 \text{ D}$.
Since it is a convex lens,the power is positive.
Therefore,the power is $+5.0 \text{ D}$.

(A) The power of a lens is defined as the reciprocal of its focal length in meters $(P = 1/f)$.
The $SI$ unit of focal length is the meter $(m)$.
Therefore,the $SI$ unit of power is $m^{-1}$,which is commonly known as the Diopter $(D)$.

(B) In an astronomical telescope,the objective lens is designed to collect as much light as possible from distant objects,which requires a large aperture and a long focal length $(f_o)$.
Conversely,the eyepiece is designed to magnify the image formed by the objective,which requires a short focal length $(f_e)$.
Therefore,the focal length of the objective is much greater than the focal length of the eyepiece $(f_o > f_e)$.

(C) An astronomical telescope consists of two lenses: an objective lens and an eyepiece.
The objective lens forms a real,inverted,and diminished image of a distant object at its focal plane.
This image acts as an object for the eyepiece,which is adjusted such that the image lies within its focal length.
The eyepiece then acts as a simple magnifier,producing a final image that is virtual,inverted,and magnified relative to the original object.
Therefore,the final image is virtual,inverted,and enlarged.

(A) simple microscope is essentially a convex lens used to view small objects.
To obtain a magnified,virtual,and erect image,the object must be placed between the optical center $(O)$ and the principal focus $(F)$ of the convex lens.
When the object is placed in this position,the light rays diverge after refraction,and when traced backward,they form a virtual image on the same side as the object.
Therefore,the correct position is between the principal focus and the optical center.

(B) In a compound microscope,the objective lens is a convex lens with a short focal length.
To obtain a real,inverted,and magnified image,the object is placed at a distance slightly greater than the focal length $(f_o)$ of the objective lens.
This image acts as an object for the eyepiece,which then produces a final virtual and highly magnified image.