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
Solution
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, F1 > F2
Hence, the correct option is C.
