Question

The radius of curvature of a convex mirror is 3.20 102 cm. An object that is 5.0 cm high is placed 53.3 cm in front of this mirror. Use a ray diagram drawn to scale to compute the following: (a) What is the location of the image? (b) What is the height of the image?

Answer 1

I can compute the answers rather than find them through ray tracing.

we use

1/p +1/q=1/f

where p=object distance =53.3 cm
q= image distance (to be found)
f=focal length = - 320 cm (the negative sign because it is convex)

we have

1/53.3 + 1/q = -1/320

1/q = -1/320 - 1/53.3 = -0.021
q=-45.68cm, the minus sign means it is a virtual image behind the mirror

the magnification is m=-q/p = -(-45.68)/53.3 = +0.857

this means it is an upright image, 0.857 times the size of the original, or the image has a height of 0.857x5cm=4.285cm