What is radius of curvature of the convex mirror?

A real object is placed at the zero end of a meterstick. A large concave mirror at the 100.0cm end of the meterstick forms an image of the object at the 70.0cm position. A small convex mirror placed at the 20.0cm position forms a final image at the 10.0cm point.

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We pressume the unkwn radius of curvature of the concave mirror at the far end of of meterstick to be R

We use the formula,1/f = 1/u+1/v, where f isthe focal length (half the radius of curvature R), u is the distance of the object from the mirror and v is the distance of the image from the mirror. Given u = 100cm and v= 70cm. So, 1/f = 1/100+1/70 =170/(100*70) = 17/700. Or f = 700/17 and R = 1400/17 = 82.3529 cm.

In the 2nd case also, the relationship between the focal lengthf,the distance of the objectu from the lens, and the distance of the image vfrom the convex lens follows the formula:

1/f = 1/u + 1/v and the radius of curvature of the lens R = 2f.

Therefore,

1/(R/2) = (u+v)/(uv). Or

R = 2uv/(u+v). Given, u = 20cm, v = 10 cm.Therefore,

R = 2*20*10/(20+10) = 400/30 = (13+1/3) cm= 13.3333 centimeter.

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