In the Fig. the direct image formed by the lens (f = 10 cm) of an object placed at O, and that formed after reflection from the spherical mirror are formed at same point O. What is the radius of curvature of the mirror?

Solution

Here,
Focal length of the lens, f = 10 cm,
Distance of object from the lens, u = –15 cm.
Let v be the distance of image I formed by the lens L.

Using lens formula,

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{10} - \frac{1}{15} = \frac{1}{30}

i.e., image is at a distance,

v = LI = 30 cm

If, I coincides with the centre of curvatureC of the mirror then, the image will be formed at I.

∴ Radius of curvature, R = PC = PI
= PL – LI
= 50 – 30
= 20 cm.

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Wave Optics

In the Fig. the direct image formed by the lens (f = 10 cm) of an object placed at O, and that formed after reflection from the spherical mirror are formed at same point O. What is the radius of curvature of the mirror?

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