A concave mirror with focal length f = 0.20 m forms an image when the object is placed at do = 0.60 m. What is di?

A concave mirror with focal length f = 0.20 m forms an image when the object is placed at do = 0.60 m. What is di?

• A. 0.60 m
• B. 0.30 m
• C. 0.10 m
• D. 1.00 m

Answer: (B)

The main idea is to use the mirror equation for a concave mirror: 1/f = 1/do + 1/di. With f = 0.20 m and do = 0.60 m, solve for di: 1/di = 1/f − 1/do = 1/0.20 − 1/0.60 = 5 − 1.666… = 3.333…, so di = 0.30 m. The positive di means the image is real and forms in front of the mirror. The magnification is m = −di/do = −0.30/0.60 = −0.50, so the image is inverted and half the size of the object. The image lies between f and 2f (between 0.20 m and 0.40 m), which is typical for a concave mirror when the object is farther than the focal point.

The main idea is to use the mirror equation for a concave mirror: 1/f = 1/do + 1/di. With f = 0.20 m and do = 0.60 m, solve for di: 1/di = 1/f − 1/do = 1/0.20 − 1/0.60 = 5 − 1.666… = 3.333…, so di = 0.30 m. The positive di means the image is real and forms in front of the mirror. The magnification is m = −di/do = −0.30/0.60 = −0.50, so the image is inverted and half the size of the object. The image lies between f and 2f (between 0.20 m and 0.40 m), which is typical for a concave mirror when the object is farther than the focal point.