Question

In a photo cell experiment, a convex lens is used to focus the light beam. Current strength is $I$. If the lens is replaced by another lens of half the diameter but same focal length, photoelectric current will be

• A. $I/2$
• B. $I/4$
• C. $I/8$
• D. $I/16$

Answer 1

Answer: (B)

Intensity of light, $1\propto d^2$
where d is the diameter of aperture of lens
$\therefore \frac{I_1}{I_2}=\frac{d_1^2}{d_2^2}=\frac{d_1^2}{{\left(d_{1}2\right)}^2}=4or,I_2=\frac{I_1}{4}$
Photocurrent $\propto$ intensity of light
Hence , $\frac{i_{p_1}}{i_{p_2}}=\frac{I_1}{I_2}or,\frac{I}{i_{p_2}}=\frac{I_1}{I_{1}4}=4$
or , $i_{p_2}=\frac{I}{4}$