JEE Advanced · 2006 · 09 Apr 2006 · Geometrical Optics

A biconvex lens of focal length f forms a circular image of sun of radius r in focal plane. Then

(A) $π r^{2} \propto f$
(B) $π r^{2} \propto f^{2}$ ✓ Correct
(C)if lower half part is covered by black sheet, then area of the image is equal to $π r^{2} /2$
(D)if f is doubled, intensity will increase

Answer: (B)

Solution

The sun subtends a small angle

α

at the lens. The radius of the image formed in the focal plane is:

r = f tan α \approx f α

Since

α

is constant (angular size of the sun), we have

r \propto f

.

Therefore, the area of the image:

π r^{2} \propto f^{2}

This is option (B).

Note: If the lower half is covered, the entire image still forms (with reduced intensity), not half the area. If f is doubled, the area increases by 4 times, so intensity (power per unit area) decreases.

JEE Advanced · 2006 · 09 Apr 2006 · Single correct option

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JEE Advanced · 2006 · 09 Apr 2006 · Geometrical Optics

Solution

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