I need help with question 7 How many times will the beam reflect from the wedge

Question

I need help with question 7

How many times will the beam reflect from the wedge surfaces? What is the final direction of the beam after the last reflection? Let s begin with a relatively simple case of a converging lens that has a focal length of 20 cm. In this example we will see how the image formed by a converging lens can change dramatically as one moves the object closer to the lens. Calculate the image distance and lateral magnification for an object at each of the following distances from the lens: (a) 50 cm, (b) 20 cm, (c) 15 cm, and (d) -40 cm. Provide the principal-ray diagram for each case.

Explanation / Answer

given f = 20 cm

a) object distance, u = 50 cm

let v is the image distance.

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/20 - 1/50

v = 33.33 cm

lateral magnification, m = -v/u = -33.33/50 = -0.67

b)

object distance, u = 20 cm

let v is the image distance.

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/20 - 1/20

v = infnite

so, image is fromed at infinite

c)

object distance, u = 15 cm

let v is the image distance.

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/20 - 1/15

v = -60 cm

lateral magnification, m = -v/u = -(-60)/15 = 4

d)

object distance, u = -40 cm

let v is the image distance.

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/20 - 1/(-40)

v = 13.33 cm

lateral magnification, m = -v/u = -13.33/(-40) = 0.333

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