A concave spherical mirror is used to create an image of an object 5.50 cm tall

Question

A concave spherical mirror is used to create an image of an object 5.50 cm tall that is located at position x = 0 cm, which is xo = 18.0 cm from point C, the center of curvature of the mirror, as shown in the figure. The magnitude of the radius of curvature for the mirror is R = 14.0 cm.

1.Calculate the position xi where the image is formed. Use the coordinate system given in the drawing.

2.What is the height hi of the image?


3.Is the image upright or inverted (upright = pointing up, inverted = pointing down)?

4.Is it real or virtual?

Explanation / Answer

Focal length = f = R/2 = 14 / 2 = 7 cm

Distance of object from mirror = Do = xo + R =18 + 14 = 32 cm

Using Mirror Equation

1/Do + 1/Di  = 1/f

1/32 + 1/Di  = 1/7

Di = 7*32/(32 - 7) = 8.96 cm

1) Position xi where image is formed = Do - Di = 32 - 8.96 = 23.04 cm

2) Hi / Ho = - Di / Do

Hi  = 5.5 x (-8.96/32) = - 1.54 cm

Height of the image = 1.54 cm

3) Since Hi is negative

Image is inverted

4) Image is real since image is formed in front of mirror and real images are formed in front of mirror

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