Question

A 28 cm tall object is placed in front of a concave mirror with a radius of 37 cm. The distance of the object to the mirror is 94 cm.
Calculate the focal length of the mirror.

Calculate the image distance.

Calculate the magnification of the image (Remember, a negative magnification corresponds to an inverted image).

Calculate the magnitude of the image height.

Answer 1

Its given that,

actual height of the object = h = 28 cm

Radius of the concave mirror = r = 37 cm

distance of the object to the mirror = o = 94 cm

(i) focal length of the mirror = f = to be determied.

Its a fact that, for a spherical mirror the focal length is always the half of the radius of curvature. So

f = r / 2 = 37 / 2 = 18.5 cm

Hence the focal length= f = 18.5 cm

(ii)let i be the image distance. So from lens eqn we know that,

1/f = 1/i + 1/o

solving the above for i we get

i = o x f / ( o - f) = 94 x 18.5 / 94 - 18.5 = 1739 / 75.5 = 23.03 cm

hence image distance = i = 23.03 cm

(iii)The magnification of image is given by

M = -i/o = -23.03/ 94 = -0.245

hence the magnification = -0.245

(iv)let h' be the image height. So we know that,

M = h'/h = i/o solving for h' we get

h' = h x i / o = 28 x 23.03 / 94 = 6.86 cm

hence height of the image = h' = 6.86 cm