Physics

Physics

Problem

Rays of light from Sun falls on a biconvex lens of focal length ff and the circular image of Sun of radius rr is formed on the focal plane of the lens. Then a. Area of image is πr2\pi r^2 and area is directly proportional of ff b. Area of image is πr2\pi r^2 and area is directly proportional to f2f^2 c. Intensity of image increases if ff is increased d. If lower half of the lens is covered with black paper area will become half
Intuitive explanation

The key insight is that the Sun's angular size, as seen from Earth, is fixed—about 0.5°. A lens collects parallel rays from the Sun and focuses them to a real image whose size depends on the focal length and that angular size. The radius rr of the solar image on the focal plane is essentially the "shadow" cast by the Sun's angular width, scaled by the lens's focal length ff. You're connecting the Sun's geometry to the geometry of the focused image through the small-angle approximation.

Intuitive explanation

The key insight is that the Sun's angular size, as seen from Earth, is fixed—about 0.5°. A lens collects parallel rays from the Sun and focuses them to a real image whose size depends on the focal length and that angular size. The radius rr of the solar image on the focal plane is essentially the "shadow" cast by the Sun's angular width, scaled by the lens's focal length ff. You're connecting the Sun's geometry to the geometry of the focused image through the small-angle approximation.

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