A student set up a magnetic optical bench with the crossed arrow target (CAT), l

Question

A student set up a magnetic optical bench with the crossed arrow target (CAT), lens, and screen. Please assume that all positions given here have offsets already included. The object on the CAT is 1.20 cm high. A CAT is placed at 20.0 cm, a lens is placed at 50.0cm, and an image 0.800 cm high is formed on a screen. (a) Calculate the magnitude of the magnification. (b) Calculate the position of the screen. (c) Calculate the focal length of the lens. (d) Calculate the new position of the lens when a second image is formed, assuming the CAT and screen are not moved. (e) Calculate the size of the image for the case in part (d).

(Please show details, especially for part d!)

Explanation / Answer

(A) Image is formed on screen so image is real.

magnification for real image will be real.

m = - hi / ho = - 0.8 cm / 1.20 cm

m = - 0.67

(B) object distance, p = 50 - 20 = 30 cm

m = - q / p = - 0.67

q = 20 cm

(C)
1/f = 1/p +1/q

1/f = 1/30 + 1/20

f = 12 cm .....Ans

(d) p + q = 50 cm (distance between CAT and screen)

1/f =1/p + 1/q

1/12 = (p + q) / p q

p (50 - p) = 12 x 50

p^2 - 50p + 600 = 0

p = 30 and 20 cm

p = 30 cm we have already taken .

now p = 20 cm

position of lens = 20 + 20 = 40 cm

(e) hi / ho = 30/20

hi = 1.5 x 1.20 = 1.8 cm

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