Question

A lamp is placed 15 cm in front of a concave spherical mirror that forms an image of the filament on a screen placed 2.85m from the mirror. What is the radius of curvature of the mirror? If the lamp filament is 5.00 mm high, how tall is its image? What is the lateral magnification?

Answer 1

Here,

object distance , do = 15 cm

image distance , di = 2.85 m

let the focal length is f

using lens formula

1/f = 1/di + 1/do

1/f = 1/15 + 1/285

f = 14.25 cm

radius of curvature of the mirror = 2 * f

radius of curvature of the mirror = 2 * 14.25 cm

radius of curvature of the mirror = 28.5 cm

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height of object , ho = 5 mm

height of image , hi = (di/do) * ho

hi = 5 * (285/15)

hi = 95 mm

the height of image is 95 mm
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lateral magnification = -di/do

lateral magnification = -285/15

lateral magnification = -19

the lateral magnification is -19