A spherical mirror forms an image of an arrow at x = x 2 = -79.1 cm. The mirror

Question

A spherical mirror forms an image of an arrow at x = x2 = -79.1 cm. The mirror is represented in the drawing as a plane at x = 0. The tip of the object arrow is located at (x,y) = (x1,y1) = (-110 cm, 7.87 cm).

1)

2)

3)

The object arrow is now moved such that image distance doubles, i.e., ximage,new = -158.2 cm. What is yimage,new, the new y co-ordinate of the image of the tip of the arrow?

4)

The object arrow is now moved to x = x1,new = -21.2 cm. What is y2,new, the new y co-ordinate of the image of the arrow?

Explanation / Answer

Part 1)

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

1/f = 1/110 + 1/79.1

f = 46.0 cm

Part 2)

h'/h = -q/p

h'/7.87 = -(79.1)/110

h' = -5.66 cm (y2)

Part 3)

1/46 = 1/p + 1/158.2

p = 64.86

h'/h = -q/p

h'/7.87 = -(158.2)/64.86

h' = -19.2 (new y2)

Part 4)

1/46 = 1/21.2 + 1/q

q = -39.3

h'/7.87 = -(-39.3)/(21.2)

h' = 14.6 cm (new y2)

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