In this example, we will find the position and magnification of an image formed by a spherical mirror. A lamp is placed 10 cmcm in front of a concave spherical mirror that forms an image of the filament on a screen placed 3.0 mm from the mirror. What is the radius of curvature of the mirror? What is the lateral magnification? If the lamp filament is 5.0 mmmm high, how tall is its image? SOLUTION SET UP (Figure 1) shows our diagram. SOLVE Both object distance and image distance are positive; we have ss = 10 cmcm and s's′ = 300 cmcm. To find the radius of curvature, we use the following: 1s+1s′110cm+1300cm==2R, and RR = 19.4 cmcm. The lateral magnification mm is obtained from m=y′/y=−s′/s m=y′y=−150mm5mm=−30. To find the height of the image, we simply multiply the height of the object by the magnification: y′=−30×5.0 m=150m REFLECT The image is inverted (as we know because m = -30 is negative) and is 30 times taller than the object. Notice that the filament is not located at the mirror’s focal point; the image is not formed by rays parallel to the optic axis. (The focal length of this mirror is ff = R/2 R/2 = 9.7 cm.) A concave mirror has a radius of curvature RR = 26 cmcm. An object of height 5.0 cmcm is placed 15 cmcm in front of the mirror. What is the image distance? What is the height of the image?
Applications Of Reflection Of Light
When a light ray (termed as the incident ray) hits a surface and bounces back (forms a reflected ray), the process of reflection of light has taken place.
Sign Convention for Mirrors
A mirror is made of glass that is coated with a metal amalgam on one side due to which the light ray incident on the surface undergoes reflection and not refraction.
In this example, we will find the position and magnification of an image formed by a spherical mirror. A lamp is placed 10 cmcm in front of a concave spherical mirror that forms an image of the filament on a screen placed 3.0 mm from the mirror. What is the radius of curvature of the mirror? What is the lateral magnification? If the lamp filament is 5.0 mmmm high, how tall is its image?
SOLUTION
SET UP (Figure 1) shows our diagram.
SOLVE Both object distance and image distance are positive; we have ss = 10 cmcm and s's′ = 300 cmcm. To find the radius of curvature, we use the following:
1s+1s′110cm+1300cm==2R,
and RR = 19.4 cmcm. The lateral magnification mm is obtained from m=y′/y=−s′/s
m=y′y=−150mm5mm=−30.
To find the height of the image, we simply multiply the height of the object by the magnification:
y′=−30×5.0 m=150m
REFLECT The image is inverted (as we know because m = -30 is negative) and is 30 times taller than the object. Notice that the filament is not located at the mirror’s focal point; the image is not formed by rays parallel to the optic axis. (The focal length of this mirror is ff = R/2 R/2 = 9.7 cm.)
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