Q.3. The convex lens and convex mirror (see figure below) have focal lengths of

Question

Q.3. The convex lens and convex mirror (see figure below) have focal lengths of +75.0 cm and -50.0 cm, respectively. An object is placed 1.00 m to the left of the lens. (a) Locate the image formed by the lens (assume the mirror to be absent): (b) Locate the image formed by the convex mirror (assuming the light not going through the lens twice);: (c) the final image, formed by light that has gone through the lens twice. State in each of the above cases whether the image is upright or inverted, real or virtual and determine the overall magnification for each of the images above. (50 Points) Object Lens Mirror 1.00 m 1.00 m

Explanation / Answer

a] Use the lens equation

1/f = 1/v + 1/u

=> 1/75 = 1/v + 1/100

=> v = 300 cm

this is the location of the image assuming no mirror ahead. The image will be inverted, real and magnified.

m = - v/u = - 300/100 = - 3

b] now, for the mirror,

1/f' = 1/v' + 1/u'

here, u' = 100 - 300 = - 200 cm

so, - 1/50 = 1/v' - 1/200

=> v' = - 66.667 cm

this image will be to the right of the mirror and the image will remain inverted but virtual.

m' = - (-66.667/-200) = - 0.333

c] object distance for the lens is now:

u'' = 100 + 66.667 = 166.667 cm

f = 75 cm

so, 1/75 = 1/v'' + 1/166.667

=> v'' = 136.363 cm = 1.3636 m

this final image is to the left of the lens and it is Real and Upright.

magnification of the image will be:

m'' = - 136.363/166.667 = - 0.818.

Overall magnification will be:

M = m x m' x m''.

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