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}} =4 or, 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} $