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Question

If AB = 10 cm & DB = 40 cm (diameter). What is the radius of curvature and the focal length of the spherical glass respectively?

A
40 cm, 10 cm
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B
40 cm, 5 cm
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C
20 cm, 20 cm
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D
20 cm, 10 cm
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Solution

The correct option is D 20 cm, 10 cm
Solution 1:
Focus is at point A since parallel rays after reflection pass through point A. Since AB is equal to 10 cm, the focal length is equal to 10 cm.
f=10 cm

Now, focal length is half the radius of curvature. So,
f=R2
R=2f=20 cm

Solution 2:
Diameter of the sphere, d=DB=40 cm
Radius of curvature is half of diameter.
R=d/2=20 cm

Now, focal length (f) is half of the radius of curvature.
f=R2=10 cm

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