The sun subtends an angle α=0.5^∘ at the pole of a concave mirror. The radius of curvature of co

step 1 Hello and welcome to this video solution of numerate. Here we are given that the sun subtend an

The sun subtends an angle α=0.5^∘ at the pole of a concave...

The sun subtends an angle $\alpha=0.5^{\circ}$ at the pole of a concave mirror. The radius of curvature of concave mirror is $R(=1.5 \mathrm{~m}) .$ The size of image formed by the concave mirror is : (a) $0.785 \mathrm{~cm}$ (b) $0.654 \mathrm{~cm}$ (c) $0.755 \mathrm{~cm}$ (d) $0.622 \mathrm{~cm}$

The sun subtends an angle $\alpha=0.5^{\circ}$ at the pole of a concave mirror. The radius of curvature of concave mirror is $R(=1.5 \mathrm{~m}) .$ The size of image formed by the concave mirror is :
(a) $0.785 \mathrm{~cm}$
(b) $0.654 \mathrm{~cm}$
(c) $0.755 \mathrm{~cm}$
(d) $0.622 \mathrm{~cm}$

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Key Concepts

Small Angle Approximation

The small angle approximation simplifies calculations in optics by assuming that for small angles (expressed in radians), the sine, tangent, and the angle itself are approximately equal. This assumption permits straightforward linear relationships between angular size and physical dimensions, such as relating the focal length and the angular size to find image size.

Angular Size

Angular size is the angle subtended by an object at a point of observation, providing a measure of its apparent size. In optical systems, when an object (or its image) subtends a small angle, the linear dimensions can be estimated by multiplying the angular size (in radians) by the distance from the observer or the relevant focal length. This conversion is critical in analyzing the dimensions of images formed by lenses or mirrors.

Concave Mirrors

Concave mirrors are curved reflective surfaces that converge incident parallel light rays to a focal point. In geometrical optics, they are characterized by their radius of curvature and focal length, where the focal length (f) of a spherical concave mirror is half of its radius of curvature (R). These properties are essential for understanding how images are formed and are used in many optical devices.

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