A single concave spherical mirror is used to create an image of a source 7.79 cm

Question

A single concave spherical mirror is used to create an image of a source 7.79 cm tall that is located at position x = 0 cm which is 37.4 cm (= 2l) to the left of Point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature for the mirror is l = 18.7 cm.

a) Calculate the position xi where the image is formed. Use the coordinate system given in the drawing.

b) What is the height hi of the image? Enter a positive result, if the image is upright (pointing up), or a negative result if the image is inverted (pointing down).

Explanation / Answer

The focal length is half the center of curvature, so f = 18.7/2 = 9.35 cm

Part A)

Apply 1/f = 1/p + 1/q

p = 37.4 + 18.7 = 56.1 cm

1/9.35 = 1/56.1 + 1/q

q = 11.22

In order of the coordinate system, that is 37.4 - 11.22 cm away'

That means that x is at 26.18 cm (round to 26.2 cm)

Part B)

h'/h = -q/p

h'/7.79 = -11.22/56.1

h' = -1.56

That means its inverted (pointing down) but your answer key wants a positive value, so enter 1.56 cm

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