In this worksheet, we will practice calculating the imaging properties of optical systems that contain both reflective and refractive components.

**Q1: **

A concave mirror with a radius of curvature 10 cm is placed 30 cm to the right of a thin, convex lens with a focal length of 15 cm. A small bulb is placed 50 cm to the left of the lens.

Find the distance to the left of the mirror of the image formed.

Find the magnification produced by the system.

**Q2: **

A lens of focal length 20 cm is placed 10 cm in front of a second identical lens. A concave mirror of focal length 15 cm is placed 50 cm behind the second lens. An object of height 3.0 cm is placed 25 cm in front of the first lens.

Find the distance in front of the mirror of the final image formed.

Find the size of the final image formed.

**Q3: **

Some telephoto cameras use a mirror rather than a lens. What radius of curvature mirror is needed to replace an 800 mm focal length telephoto lens?

**Q4: **

An object of height 5.00 cm is placed 55.0 cm in front of a diverging lens of focal length 46.0 cm. Behind the lens, there is a convex mirror of focal length 18.0 cm placed 36.0 cm from the converging lens.

Find the location of the final image from the mirror.

Find the size of the final image.

**Q5: **

An object of height 5.00 cm is placed at 29.0 cm in front of a converging lens of focal length 23.0 cm. Behind the lens, there is a concave mirror of focal length 23.0 cm. The distance between the lens and the mirror is 8.00 cm.

Find the location of the final image from the mirror.

Find the size of the final image.

**Q6: **

You photograph a 1.80 m tall person with a camera that has a 6.30 cm focal length lens. The image on the camera’s photosensor must be no more than 3.50 cm high. What must the minimum distance from the person to the lens be?

**Q7: **

A point source of light is located 59.0 cm in front of a converging lens of focal length 32.0 cm. A concave mirror with a focal length of 24.0 cm is placed 26.0 cm behind the lens. What is the total magnification?