A concave mirror (R = 56.0 cm) is used to project a transparent slide onto a wal

Question

A concave mirror (R = 56.0 cm) is used to project a transparent slide onto a wall. The slide is located at a distance of 33.0 cm from the mirror, and a small flashlight shines light through the slide and onto the mirror. The setup is similar to that in the figure. (a) How far from the wall should the mirror be located? cm (b) The height of the object on the slide is 1.30 cm. What is the height of the image? cm (c) How should the slide be oriented, so that the picture on the wall looks normal? The slide should be right side up. The slide should be upside down.

Explanation / Answer

Given

   concave mirror of radius of curvature R = 56 cm, the focal length is f = R/2 = 56/2 = 28 cm
the slide located at a distance from the mirror is s = 33 cm

the image of the slide is forming on the wall , the image distance s' =?

from the equation
a)

       1/s+1/s' = 1/f

       1/s' = 1/f -1/s

       = 1/28 -1/33

       s' = 184.8 cm = 1.848 m

the mirror should be located at 1.848 m from the wall.

b)
   the height of the object is y = 1.30 cm , height of the image is y' =?

from lateral magnification m = -s'/s = y'/y

           y' = -s'*y/s
             
                = - 184.8*1.3/33 cm

= - 7.28 cm

-ve sign indicates the image is inverted image

c) in order to look the picture normal on the wall the slide should be upside down, so the image will be normal on the wall

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