Question

# A 31 cm tall object is placed in front of a concave mirror with a radius...

A 31 cm tall object is placed in front of a concave mirror with a radius of 32 cm. The distance of the object to the mirror is 88 cm.
Calculate the focal length of the mirror.

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Calculate the image distance.

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

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Calculate the magnitude of the image height.

given that,

actual height of the object = h = 31 cm

Radius of the concave mirror = r = 32 cm

distance of the object to the mirror = o = 88 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 = 32 / 2 = 16 cm

Hence the focal length= f = 16 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) = 88 * 16 / 88 - 16 = 1408 / 72 = 19.55 cm

hence image distance = i = 19.55 cm

(iii)The magnification of image is given by

M = -i/o = -19.55/ 88 = -0.222

hence the magnification = -0.222

(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 =31* 19.55 / 88 = 6.88 cm

hence height of the image = h' = 6.88 cm

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