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Chapter 23: Problem 74

A point source of light is placed \(10 \mathrm{cm}\) in front of a concave mirror; the reflected rays are parallel. What is the radius of curvature of the mirror?

Short Answer

Expert verified
Answer: The radius of curvature of the concave mirror is -20 cm.

Step by step solution

01

Identifying given values

We are given that the point source of light is placed 10 cm in front of the mirror (object distance), and the reflected rays are parallel to each other (image distance is infinite). Therefore, Object distance (u) = -10 cm (negative sign since the object is on the left side of the mirror) Image distance (v) = ∞
02

Using the Mirror formula

According to the mirror formula, 1/f = 1/u + 1/v Since the reflected rays are parallel, the focal length (f) is equal to half the radius of curvature (R). So, we can also rewrite the formula as, 1/(R/2) = 1/u + 1/v
03

Plug in the given values and solve for R

Now, let's plug in the values we know and solve for the radius of curvature (R). 1/(R/2) = 1/(-10) + 1/∞ 1/(R/2) = (-1/10) Now, we solve for R, R/2 = -10 R = -20 cm The radius of curvature of the concave mirror is -20 cm. The negative sign indicates that it is a concave mirror.

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