A concave mirror has a focal length of 42 cm. The image formed by a mirror is 97

Question

A concave mirror has a focal length of 42 cm. The image formed by a mirror is 97 cm in front of the mirror. On the diagram below indicate reflecting and non-reflecting surfaces and presents of optical center, geometrical center, and focal point. Find the radius of curvature of this mirror. Using the given data determine the object distance? Determine the magnification that is produced by the mirror. Describe the optical image that was formed by the mirror. Present the ray diagram for the situation that you have here.

Explanation / Answer

as it is a concacve mirror , the surface that faces the image is reflecting surface and the surface that faces away from the image is non-reflecting surface.

optical center=focal length=42 cm from the surface

geometrical center=radius of curvature=2*focal length=84 cm

focal point =42 cm from the surface

b)radius of curvature=84 cm from the surface

c)

the following sign convention is used.

distance to the right of the mirror is negative.

height above the plane of mirror is positive.

then object distance=-u(let)
image distance=v=-97 cm

focal length=f=-42 cm
using mirror equation:

(1/v)+(1/-u)=1/f
u=74.073 cm

so object distance is 74.073 cm from the surface towards the right side.

d)magnification=-image distance/object distance=-0.763

e)as magnification is -ve, the image is inverted
as it is in the same side of the object, the image is real.

as magnification is less than 1, the size is less than object size.

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