Expert Q&A; Done As part of an instrument you are building, you need an optical

Question

Expert Q&A; Done As part of an instrument you are building, you need an optical system which will project an enlarged image of an object on a screen. You build this projector out of two convex lenses. Lens 1 is closest to the object and has focal length fl -3cm. Lens 2 is a distance d- 10cm from lens 1 and has focal length f2-20cm. While your instrument is running, the object is 2.5cm from lens 1 (a)For the device to function must the final image of the device be real or virtual? Explain. (b)Compute the final image location. Clearly show any intermediate calculations you needed. (c)Compute the total magnification of the device. (d)Describe the image formed by the device. Justify your description by your calculation (e)For the object distance given, could you project the image from the first lens only on the screen and save vourself the use of the second lens? Whv or whv not?

Explanation / Answer

a) The Image must be real. Because, virtual image can not be captured on the screen.

b)
let

f1 = 3 cm

u1 = 2.5 cm

f2 = 20 cm

d = 10 cm

let v1 is the image distance from the first lens

apply, 1/u1 + 1/v1 = 1/f1

1/v1 = 1/f1 - 1/u1

1/v1 = 1/3 - 1/2.5

v1 = -15 cm

magnification, m1 = -v1/u1

= -(-15)/2.5

= 6

object distance for the second lens, u2 = 10 + 15

= 25 cm

let v2 is the image distance.

use,

1/u2 + 1/v2 = 1/f2

1/v2 = 1/f2 - 1/u2

1/v2 = 1/20 - 1/30

v2 = 60 cm (final image location) <<<<<<<<<<<--------------------Answer

magnification, m2 = -v2/u2

= -60/30

= -2

c) Total magnification, m = m1*m2

= 6*(-2)

= -12

d) The final image formed on the screen is inverted. Because, magnification overall magniifcation is negative.

e) No. Because the image produced by first lens is virtual which we can not capture on the screeen.

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