Question

A student has obtained a highly diminished image of the Sun on a screen using a convex lens. In order to determine the focal length of the lens, what should he measure?

• A. Curvature of the two surfaces of the lens
• B. Aperture of the lens
• C. Distance of the screen from the lens
• D. Radius of curvature of the two surfaces of the lens​

Answer 1

The correct option is C

Distance of the screen from the lens

• Object distance that is the distance of the Sun from the lens can be considered as, $u=\infty$
• The focal length can be obtained by the formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Correct answer explanation:

• Substituting the known value to the above-mentioned formula,

$$\begin{gathered} \frac{1}{v}-\frac{1}{\infty }=\frac{1}{f} \\ \Rightarrow \frac{1}{v}-0=\frac{1}{f} \\ \Rightarrow f=v \end{gathered}$$

• Here, $v$ is the distance of the screen from the convex lens.
• Thus, to determine focal length, screen distance from the lens should be measured.

Incorrect answer explanation:

• Option A is incorrect as only the curvature of two surfaces of the lens has no direct relationship with the focal length.
• Option A is incorrect as only the aperture of the lens is not enough to determine the focal length.
• Option A is incorrect as only the radius curvature of two surfaces of the lens is not enough to determine the focal length.

Thus, option C is correct.