A spherical mirror forms an image of an arrow at x = x 2 = -79.3 cm. The mirror

Question

A spherical mirror forms an image of an arrow at x = x2 = -79.3 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) = (-104 cm, 6.18 cm).

1)What is f, the focal length of the mirror? If the mirror is concave f is positive. If the mirror is convex, f is negative.

2)What is y2, the y-coordinate of the image of the tip of the arrow?

3)The object arrow is now moved such that image distance doubles, i.e., ximage,new = -158.6 cm. What is yimage,new, the new y-coordinate of the image of the tip of the arrow?

4)The object arrow is now moved to x = x1,new = -25.2 cm. What is y2,new, the new y-coordinate of the image of the arrow?

Explanation / Answer

ANSWER

Part 1)

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

1/f = 1/104 + 1/79.3

f = 44.99 cm

Part 2)

h'/h = -q/p

h'/6.18 = -(79.3)/104

h' = -4.71 cm (y2)

Part 3)

1/44.99 = 1/p + 1/158.6

p = 62.81

h'/h = -q/p

h'/6.18 = -(158.6)/62.81

h' = -15.60 (new y2)

Part 4)

1/44.99 = 1/25.2 + 1/q

q = -57.29

h'/6.18 = -(-57.28)/(25.2)

h' = 14.05 cm (new y2)

Regards!!!

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