Question

A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in the central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:

• A. \(f,\; \dfrac{I}{4}\)
• B. \(\dfrac{3f}{4},\; I\)
• C. \(f,\; \dfrac{3I}{4}\)
• D. (f)/(2), (I)/(2)

Hint:

• Aperture affects intensity • Focal length depends only on lens geometry

Answer 1

The Correct Option is C

Step 1: Focal length of a thin lens depends only on refractive index and curvatures, not on aperture. ⟹ f remains unchanged
Step 2: Original aperture area: A=π((d)/(2))²=(π d²)/(4)
Step 3: Blocked central area: Ab=π((d)/(4))²=(π d²)/(16)
Step 4: Transmitting area: A'=(3π d²)/(16)
Step 5: Intensity ∝ aperture area: I'=(A')/(A)I=(3)/(4)I