Sun subtends an angle of 0.5^∘ at the centre of curvature of a concave mirror of radius of curva

step 1 It has been given that sun substants 0 .5 degree angle at the center of curvature at the center

Sun subtends an angle of 0.5^∘ at the centre of curvature of...

Sun subtends an angle of $0.5^{\circ}$ at the centre of curvature of a concave mirror of radius of curvature $15 \mathrm{~m}$. The diameter of the image of the sun formed by the mirror is
(a) $8.55 \mathrm{~cm}$
(b) $7.55 \mathrm{~cm}$
(c) $6.55 \mathrm{~cm}$
(d) $6.55 \mathrm{~cm}$

Key Concepts

Concave Mirror

A concave mirror is a reflective surface that curves inward, resembling the interior of a sphere. It has the property of converging parallel light rays to a focal point, and it is widely used in optical devices like telescopes, flashlights, and solar concentrators. Its behavior is governed by mirror formulas that relate object distance, image distance, and focal length.

Radius of Curvature and Focal Length

The radius of curvature of a spherical mirror is the distance from the mirror’s surface to the center of the sphere it is part of. For a concave mirror, the focal length is half of the radius of curvature, which is a crucial relationship in determining where and how the image is formed. This concept is key to understanding the focusing properties and image magnification in spherical mirrors.

Image Formation from Distant Objects

When an object is very far away, its rays can be considered parallel, meaning that they converge at the focal point of a concave mirror. This leads to the formation of a real and inverted image at the focal point. The properties of the image, including its size, are determined by the focal length and the object's angular diameter.

Angular Size and the Small Angle Approximation

Angular size is a measure of how large an object appears from a given point of view, typically expressed in degrees or radians. For small angles, the small angle approximation allows us to approximate the physical size of an image by multiplying the focal length by the angle in radians. This concept is essential in optical systems for relating the dimensions of distant objects, like the sun, to the dimensions of their images formed by lenses or mirrors.

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