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A student has obtained an image of a distant object on a screen to determine the focal length F_{1} of the given lens. His teacher, after checking the image, gave him another lens of focal length F_{2} 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 F_{1} < F_{2}

(B) Convex and F_{1} < F_{2}

(C) Convex and F_{1} > F_{2}

(D) Concave and F_{1} > F_{2}

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#### 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 F_{2}.

Hence, F_{1} > F_{2}

Hence, the correct option is C.

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