A spherical mirror forms an image of an arrow at x = x 2 = -73.3 cm. The mirror

Question

A spherical mirror forms an image of an arrow at x = x2 = -73.3 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) = (-88 cm, 3.55 cm).

3.) The object arrow is now moved such that image distance doubles, i.e., ximage,new = -146.6 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 = -21.6 cm. What is y2,new, the new y co-ordinate of the image of the arrow?

Explanation / Answer

This is a concave spherical mirror, Because for convex mirror you can not get get image on the same side of the object.

To find focal length f, use equation,

1/f = 1/u + 1/v ----------------(1)

1/f = 1/73.3 + 1/88      => f= 40 cm

3) Put u=146.6cm in (1)

1/40 = 1/146.6 + 1/v    => v= 55cm    to the left of the mirror or y2new= - 55cm

4) Put u=21.6 cm in (1)

1/40 = 1/21.6 + 1/v    => v= 46.96cm    to the right of the mirror or y2new = + 46.96cm

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