A spherical mirror forms an image of an arrow at x = x 2 = -77.3 cm. The mirror

Question

A spherical mirror forms an image of an arrow at x = x2 = -77.3 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) = (-92 cm, 6.08 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 co-ordinate 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 = -154.6 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 = -23.1 cm. What is y2,new, the new y co-ordinate of the image of the arrow?

Explanation / Answer

1) 1/p + 1/q = 1/f

1/92 + 1/77.3 = 1/f
f=42 cm

2) y2 = -q y/p = -77.3*6.08/92= - 5.11 cm

3)

1/p + 1/154.6 = 1/42
p=57.67

y = -154.6*6.08/57.67= -16.3 cm

4)
1/q + 1/23.1 = 1/42

q=-51.33 cm

y = 51.33*6.08/23.1= 13.51 cm

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