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 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 ${F_1} > {F_2}$

Hint:Sharp image of a distant object is formed at focus of the lens so in order to form the image on the screen, the screen must be placed at the focus of the mirror. In the second case the lens is moved away from the screen to obtain a sharp image; it means focal length in the second case must be larger.

Complete answer:
Since image is formed at screen it means image formed is real and only convex lens forms real image for a real object hence lens must be convex. For distant objects incident rays coming from the distant object to the lens are almost parallel to the principal axis of the lens it means the image formed by the lens of the distant object must be at focus.

Therefore ${F_1}$ must be the distance between lens and screen in the first case. After his teacher checked the image and gave him another lens of focal length ${F_2}$ then in this case too. Distance between lens and screen should be the focal length of the lens or ${F_2}$ and in this case lens has to move away from the screen it means focal length in this case must be larger as compared to previous case because focal length is equal to distance between lens and the screen in both cases for image of all distant objects.

Hence the correct answer is Option B.

Note: Image formed on screen implies image is real which tells us about the nature of lens which is convex lens and distance between lens and screen tells us about the focal length of the lens larger the distance implies larger the focal length.