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
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.
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
I hope help you.
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