Question

The lens of a slide projector has a focal length of +12.0 cm. a slide 12.6 cm to the left of the lens forms the object for the lens. the screen should be placed a. 25.2 cm to the left of the lens. b. 252 cm to the right of the lens. c. 25.2 cm to the right of the lens. d. 395 cm to the right of the lens.

Answer 1

The correct answer is a.) The screen should be placed 25.2 cm to the right of the lens.

Step-by-step explanation:

In this question, we are given that the focal length of the lens is +12.0 cm and the slide is placed 12.6 cm to the left of the lens. We need to determine where the screen should be placed.

According to the lens equation, 1/f = (1/v) - (1/u), where f is the focal length, v is the image distance, and u is the object distance. Since the lens is converging (positive focal length), u will be negative.

Plugging in the given values into the lens equation, we have 1/12.0 = (1/v) - (1/-12.6). Solving for v, we get v = -25.2 cm. Since the screen should be on the opposite side of the lens as the object, the screen should be placed 25.2 cm to the right of the lens.

Answer 2

The screen should be placed 25.2 cm to the left of the lens.

Step-by-step explanation:

For a slide projector, the image formed by the lens should be projected onto the screen. Using the lens formula
`\((1)/(f) = (1)/(d_o) + (1)/(d_i)\), where \(f\) is the focal length, \(d_o\)` is the object distance, and \(d_i\) is the image distance, we can find the image distance.

Given the focal length (\(f = +12.0\) cm) and the object distance (\(d_o = 12.6\) cm to the left of the lens), we can solve for the image distance.

`\((1)/(f) = (1)/(d_o) + (1)/(d_i)\)\((1)/(12) = (1)/(12.6) + (1)/(d_i)\)\((1)/(d_i) = (1)/(12) - (1)/(12.6)\)\((1)/(d_i) = (5)/(756)\)\(d_i = (756)/(5) = 151.2\) cm`

The image is formed 151.2 cm to the left of the lens. To project this image onto the screen, the screen should be placed at a distance equal to the image distance on the opposite side of the lens. Thus, the screen should be located 25.2 cm to the left of the lens (\(151.2 - 126 = 25.2\) cm).

Therefore, the correct placement for the screen is 25.2 cm to the left of the lens.