A concave mirror has a radius of curvature equal to 24 cm. Use ray diagrams to l

Question

A concave mirror has a radius of curvature equal to 24 cm. Use ray diagrams to locate the image, if it exists, for an object near the axis at the distances labeled below. For each of the following cases, state whether the image is real or virtual, upright or inverted, and enlarged, reduced, or the same size as the object. (Do this on paper as well. )

(a) 55 cm real ,virtual ,upright ,inverted, enlarged reduced same size as object there is no image
(b) 24 cm real virtual upright inverted enlarged reduced same size as object there is no image
(c) 12 cm real virtual upright inverted enlarged reduced same size as object there is no image
(d) 8 cm real virtual upright inverted enlarged reduced same size as object there is no image

Explanation / Answer

R = 24 cm, Focal length f = R /2 = 24 / 2 = 12 cm
a) u = 55 cm Image distance is 1 / v = 1/ f - 1/ u
= 1/12 - 1/55
= 0.0651
v = 15.35 cm
Magnefication is M = - v/ u
= - 15.35 / 55
M = -0.28
The image is virtual, upright, and reduced
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b)u = 24cm
Objectdistance is 1 / v = 1/f - 1/u
= 1/ 12 - 1/24
v = 24 cm
Magneficationis M = -24 /24
M = -1.0
The image is virtual, upright, and reduced
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c) u = 12 cm
1/v = 1/f - 1/u = 1/12 - 1/12 = 0
v = 0 [undefined]
Magnification M = 0[undefined]
The image is virtual, upright, and reduced
--------------------------------------------------
d)u = 8cm
Objectdistance is 1 / v = 1/f - 1/u
v = -0.2 cm
Magneficationis M = -24 /8
M = 3.0
The image is virtual, upright, and reduced

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