Question

A student has obtained an image of a distant 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 F₁ < F₂
• B. Convex and F₁ < F₂
• C. Convex and F₁ > F₂
• D. Concave and F₁ > F₂

Answer 1

The correct option is C

Convex and F₁ > F₂

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
$\frac{1}{F}=\frac{1}{v}-\frac{1}{u}$
$\Rightarrow F=\frac{uv}{u-v}$
For convex lens, object distance = -u
Image distance = +v
$\Rightarrow F=\frac{uv}{u+v}$
where F is the focal length of the lens.
Therefore, F is lesses for the second lens of focal length $F_2$
Hence, $F_1$ > $F_2$