Chapter 34: Q 70 (page 993)

An old-fashioned slide projector needs to create a 98-cm-high image of a 2.0-cm-tall slide. The screen is 300 cm from the slide.
a. What focal length does the lens need? Assume that it is a thin lens.
b. How far should you place the lens from the slide?

Short Answer

Expert verified

a) Focal length of the lens is 5.9 cm

b) The lens is located at a distance of 6.0 cm from the slide and 294 cm from the screen.

Step by step solution

Step 1. Given information is :

Height of the image, h' = 98 cm

Height of the slide, h = 2 cm

Distance between the slide and the screen = 300 cm

We need to find out :

a) Focal length of the lens

b)The distance s' between slide and the lens

Step 2. Using Magnification concept,

$|M| = \frac{h'}{h} h' a n d h a r e i m a g e a n d o b j e c t h e i g h t r e s p e c t i v e l y . |M| = \frac{98 c m}{2.0 c m} = 49$ M is the Magnification.

Step 3. Magnification in terms of object and image distance

$M = - \frac{s'}{s} w h e r e s' a n d s a r e i m a g e a n d o b j e c t d i s \tan c e r e s p e c t i v e l y . I t i s g i v e n t h a t s + s' = 300 c m s' = 300 c m - s M = - \frac{300 c m - s}{s} - 49 = - \frac{300 c m - s}{s} 49 = \frac{300 c m - s}{s} 49 s = 300 c m - s 50 s = 300 c m s = \frac{300 c m}{50} = 6.0 c m A n d s' = 300 c m - s = 300 c m - 6.0 c m = 294 c m$

Step 4. Using thin lens formula

$\frac{1}{s} + \frac{1}{s'} = \frac{1}{f} \frac{1}{f} = \frac{s' + s}{s s'} f = \frac{s s'}{s' + s} f = \frac{(6.0 c m) (294 c m)}{6.0 c m + 294 c m} f = 5.9 c m$

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An old-fashioned slide projector needs to create a 98-cm-high image of a 2.0-cm-tall slide. The screen is 300 cm from the slide.
a. What focal length does the lens need? Assume that it is a thin lens.
b. How far should you place the lens from the slide?

Short Answer

Step by step solution

Step 1. Given information is :

Step 2. Using Magnification concept,

Step 3. Magnification in terms of object and image distance

Step 4. Using thin lens formula

One App. One Place for Learning.

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An old-fashioned slide projector needs to create a 98-cm-high image of a 2.0-cm-tall slide. The screen is 300 cm from the slide.a. What focal length does the lens need? Assume that it is a thin lens.b. How far should you place the lens from the slide?

Short Answer

Step by step solution

Step 1. Given information is :

Step 2. Using Magnification concept,

Step 3. Magnification in terms of object and image distance

Step 4. Using thin lens formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

Electric Charge Field and Potential

Waves Physics

Fields in Physics

Space Physics

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.

An old-fashioned slide projector needs to create a 98-cm-high image of a 2.0-cm-tall slide. The screen is 300 cm from the slide.
a. What focal length does the lens need? Assume that it is a thin lens.
b. How far should you place the lens from the slide?