Question

A student has obtained an image of a distant object on a screen to determine the focal length F₁ of the given lens. His teacher, after checking the image, gave him another lens of  focal length F₂ and asked him to focus the same object on the same screen. The student found that to obtain a sharp image, he has to move the lens away from the screen. From this finding, we may conclude that both the lenses given to the student were :

(A) Concave and F₁ < F₂

(B) Convex and F₁ < F₂

(C) Convex and F₁ > F₂

(D) Concave and F₁ > F₂

Answer 1

The lens is convex, as it forms real image. As mentioned  in the second case, the image distance (v) is increasing; hence, the object distance (u) is decreasing.

The lens formula is

`1/F=1/v-1/u`

`rArrF=(uv)/(u-v)`

For convex lens, object distance = -u

Image distance = + v

`rArrF=(uv)/(u+v)`

where F is the focal length of the lens.

Therefore, F is lesser for the second lens of focal length F₂.

Hence, F_​1 > F₂

Hence, the correct option is C.