Two lenses that are L = 37 cm are used to form an image, as shown in figure. Len

Question

Two lenses that are L = 37 cm are used to form an image, as shown in figure. Lens 1 is converging and has a focal length f_1 = 14 cm; lens 2 is diverging and has a focal length f_2 = -7.0 cm. 33.6 Determine the distance from lens 1 to the final image. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, cm What is the magnification of this image? -0.965 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.

Explanation / Answer

Here, f1 = 14 cm

f2 = -7 cm

L = 37 cm

a) after the first lens

let the image location is di1

Using lens formula

1/f = 1/di1 + 1/do1

1/14 = 1/24 + 1/di1

di1 = 33.6 cm

Now , for the second lens

object distance , do2 = 37 - 33.6 = 3.4 cm

Using lens formula

1/f2 = 1/di2 + 1/do2

-1/7 = 1/3.4 + 1/di2

di2 = -2.29 cm

Now , distance of final image to lens 1 = 37 - 2.29

distance of final image to lens 1 = 34.71 cm

the distance of final image to lens 1 is 34.71 cm

b)

magnification = 33.6 * 2.29/(3.4 * 24)

magnification = 0.943

the magnification is 0.943

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