A laser is mounted as shown in the figure (distances d and h are given) above th

Question

A laser is mounted as shown in the figure (distances d and h are given) above the axis of a converging lens with positive focal length f. The laser beam travels parallel to the axis of the lens. A large screen is placed at a distance ds to the right of the lens. The laser beam passes through the lens and makes a dot on the screen at a distance hs, measured upward from the axis of the lens. Assume that a positive value means that the dot is above the axis, while a negative value means that the dot is below the axis.

A) Find the distance hs.

Express your answer in terms of some or all of the variables d, h, f, and ds. Note that not all of the variables may be required for the answer. The correct answer does not depend on: d, s.

B) Now consider a specific case. Let the laser be 50 centimeters to the left of the lens and at height 15 centimeters above the axis of the lens. The lens has focal length 30 centimeters, and the screen is 1 meter to the right of the lens.

What is the position hs of the dot on the screen? Express your answer in centimeters, to two significant figures.

Explanation / Answer

a)

hs = -h ( ds - f) / f

the sign of the height depends upon the sign of . If the focal point is in front of the screen, the dot will be below the axis of the lens. If the focal point is on the screen, the image will be at the level of the axis of the lens, and if the focal point is behind the screen, the dot will be above the axis of the lens

b)

hs = -35 cm

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