Mirror and Lens

Question

An object is positioned 26 cm from a spherical concave mirror of unknown focal length. The image that is formed is 60 cm from the mirror.

If 60 cm corresponds to the positive image distance, calculate the focal length.

If the object is 30 cm tall, determine the height of the image.

If 60 cm corresponds to the negative image distance, calculate the focal length.

If the object is 30 cm tall, determine the height of the image.

Answer 1

Part 1 Using di=+60, d0=26, we get 1/f=1/26+1/60 so f = 18.14 cms

Part 2 Magnification = di/d0 =-60/26 = - 2.31, if the object is 30 cms, ht of image is -2.31 * 30 = -69.2 cms (The negative sign means it is inverted and real)

Part 3 1/f=1/26-1/60 so f = 45.9

Part 4 Magnification is the same but this time it is positive so it is virtual and upright. Size is 69.2 cms