# Worksheet: Reflected Images

In this worksheet, we will practice explaining the formation of images by focusing light rays in mirrors that have different radii of curvature.

Q1:

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away?

Q2:

A light bulb is placed between a plane mirror and a convex mirror that has a radius of curvature of 8.0 cm. The distance from the plane mirror to the vertex of the convex mirror is 30 cm, along the mirror’s optical axis. The plane mirror is located 10 cm from the bulb, also along the convex mirror’s optical axis. The system forms multiple images.

Find the distance from the vertex of the convex mirror to the first image that produced by the convex mirror.

Find the position of the second image formed by the convex mirror.

Q3:

An electric room heater uses a concave mirror to reflect infrared radiation from hot coils. The mirror in a heater has a radius of curvature of 50.0 cm and produces an image of the coils 3.00 m away from the mirror. How far from the curved mirror are the coils located?

Q4:

Some heating coils are located 27.3 cm from the vertex of a concave mirror, along the mirror’s optical axis. The heating element radiates 1.50 kW of infrared radiation and has an area of 100 cm2. Half of the radiated power is reflected and focused by the mirror. If the mirror has a magnification of , what is the intensity of infrared radiation projected by the mirror onto a person standing 3.00 m from the mirror’s vertex, along the mirror’s optical axis?

Q5:

Calculate the focal length of a mirror formed by the shiny back of a spoon that has a 4 cm radius of curvature.

Q6:

A shopper standing 5.00 m from a convex security mirror sees his image magnified by a factor of 0.250.

What is the focal length of the mirror?

What is the mirror’s radius of curvature?

Q7:

An object is located 6.0 cm from the vertex of a glass concave surface with a radius of curvature of 25 cm. Find the magnification of the image produced by reflection from the surface. Use a value of 1.5 for the refractive index of glass.

Q8:

An object is immersed in water at a distance of 25 cm from the vertex of a glass concave surface with a radius of curvature of 10 cm. Find the magnification of the image produced by reflection from the surface. Use a value of 1.5 for the refractive index of glass and a value of 1.33 for the refractive index of water.

Q9:

An object is located in air 40 cm from the vertex of a glass concave surface with a radius of curvature of 15 cm. Find the magnification of the image produced by reflection from the surface. Use a value of 1.5 for the refractive index of glass.

Q10:

Consider a pair of flat mirrors that are positioned so that an angle of is made between the sides of the mirror in contact with each other. An object is placed between the mirrors on a line that passes through the point where the sides of the mirrors are in contact, equidistant from each mirror. How many images of the object are formed in both mirrors?

Q11:

A 3.0 cm tall object is placed 5.0 cm in front of a convex mirror of radius of curvature 20 cm.

How far from the mirror is the image formed?

What is the height of the image formed?