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An object is placed 9.5 cm in front of a convex spherical mirror. Its image forms 3.2 cm behind the mirror. What is the radius of curvature of the mirror? Show all work.

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Using the mirror formula.

1/v + 1/u = 1/f

1/9.5 + 1/3.2 = 1/f

1/f = 3.2 + 9.5 / 9.5 * 3.2

1/f = 4.82 cm

Radius = 2f

Radius = 2 x 4.82

Radius = 9.64 cm

Answer:

Radius of curvature, R =  9.64 cm              

Explanation:

It is given that,

Object distance, u = -9.5 cm

Image distance, v = 3.2 cm

We have to find the radius of curvature of the mirror. The relationship between focal length and the radius of curvature as R = 2 f where f is the focal length of the mirror.

Using Mirror's formulas as :

[tex]\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}[/tex]

[tex]\dfrac{1}{3.2}+\dfrac{1}{-9.5}=\dfrac{1}{f}[/tex]

f = 4.82 cm

And radius of curvature of the mirror becomes, R = 9.64 cm. Hence, this is the required solution.

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