To find the focal length of a convex mirror, a student records the following data.
Object Pin Convex Lens Convex Mirror Image Pin
22.2 cm 32.2 cm 45.8 cm 71.2 cm

The focal length of the convex lens is f₁ and that of mirror is f₂. Then taking index correction to be negligibly small, f₁ and f₂ are close to

Question

To find the focal length of a convex mirror, a student records the following data.
Object Pin - Convex Lens - Convex Mirror - Image Pin; 22.2 cm - 32.2 cm - 45.8 cm - 71.2 cm
The focal length of the convex lens is f₁ and that of mirror is f₂. Then taking index correction to be negligibly small, f₁ and f₂ are close to

Accepted Answer

(1) f₁=7.8 cm, f₂=12.7 cm. Step 1: the lens. u=32.2-22.2=10 cm and v=71.2-32.2=39 cm. 1/(f₁)=1/(10)+1/(39)=0.1+0.0256=0.1256, so f₁≈8 cm, i.e. close to 7.8 cm. Step 2: the mirror. With the mirror in place the final image coincides with the object, so the converging beam must be aimed at the mirror's centre of curvature. Without the mirror that beam would meet at the image pin, 71.2 cm. R=71.2-45.8=25.4 cm. f₂=R/2=12.7 cm.

Step-by-step solution

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