Question

A .5cm tall christmas tree light is 21cm to the left of a spherical christmas tree ornament, which has a diameter of 6cm. The outside of the ornament acts as a convex mirror.

a)Is the center of the curvature on the same side or the opposite side of the reflected light. What does this tell you of the sign of the radius of curvature of the mirror.

b) find the distance of the image of the tree light relative to the ornament and state whether it is on the same side of the ornament face as the tree light or the opposite side.

c)Find the height of the image of the tree light and state if it is upright or inverted.

More than answer, a brief explanation would be preferred. At the very least formulas used to obtain answer, plase.

Answer 1

a) The centre of curvature of a convex mirror is on the opposite side of the reflected light. That's why the sign of the radius of curvature of a convex mirror is negative.

b) Mirror formula: 1/d_o + 1/d_i = 1/f

Here, d_o = object distance = 21 cm

f = focal length of the convex mirror = R/2 = -(6 / 2) / 2 = -1.5 cm

Putting these values in the mirror formula, we get,

1/21 + 1/d_i = 1/(-1.5)

=> d_i = -21 * 1.5 / (21 + 1.5) = -1.4 cm

Since the image distance is negative, it is virtual and it is formed in the direction opposite to the direction of the reflected light i.e. on the opposite side of the ornament face.

c) We have,

h_i/h_o = -d_i/d_o

=> image height, h_i = -h_od_i/d_o = -0.5 * (-1.4) / 21 = 0.033

Since image height is positive, image is upright relative to the object.