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Q. 78

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 994

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Short Answer

A spherical mirror of radius R has its center at C, as shown in FIGURE P34.78. A ray parallel to the axis reflects through F, the focal point. Prove that f = R/2 if

The statement is proved.

See the step by step solution

Step by Step Solution

Step 1: Given information

We have given,

Radius of the spherical mirror=R

A ray incident parallel to the principle axis and reflects through F.

we have to prove

Step 2: Simplify

According to the law of reflection

incident angle = Reflected angle

As incident angle is parallel to the principle axis.

then using the figure, we can say that the alternative angles are equal.

since two angle of the triangle are equal then we can say that it is a isosceles triangle.

CF=FA

and CM=MA=

since pole to C length is R.

since,

then we write,

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