Two identical converging lenses having focal lengths of 20.0 cm. They are initially separated by a distance of 5.00 cm. A distance of 171 cm separates a stationary object and screen to view an image. The lenses are located inbetween the object and screen such that the nearest lens is a distance of 45.0 cm from the object. At t = 0, the lens furthest from the object is moving at a constant rate of 0.5 cm/s toward the screen. At what time will there first be a focused image on the screen? Enter a number measured in seconds.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement: Two Converging Lenses and Focused Image Calculation**

Two identical converging lenses having focal lengths of 20.0 cm. They are initially separated by a distance of 5.00 cm. A distance of 171 cm separates a stationary object and screen to view an image.

The lenses are located in between the object and screen such that the nearest lens is a distance of 45.0 cm from the object. At \( t = 0 \), the lens furthest from the object is moving at a constant rate of 0.5 cm/s toward the screen.

**Question:**
At what time will there first be a focused image on the screen? Enter a number measured in seconds.

**Analysis:**

1. **Lens Placement:** 
   - Nearest lens is 45.0 cm from the object.
   - Second lens is initially 5.00 cm further from the nearest lens.

2. **Movement:** 
   - Second lens moves at 0.5 cm/s towards the screen.

**Calculations:**

To solve this, you must use lens equations to determine when the image is focused on the screen as the second lens moves. Consider the focal length, distances involved, and the rate of movement to determine the time \( t \).
Transcribed Image Text:**Problem Statement: Two Converging Lenses and Focused Image Calculation** Two identical converging lenses having focal lengths of 20.0 cm. They are initially separated by a distance of 5.00 cm. A distance of 171 cm separates a stationary object and screen to view an image. The lenses are located in between the object and screen such that the nearest lens is a distance of 45.0 cm from the object. At \( t = 0 \), the lens furthest from the object is moving at a constant rate of 0.5 cm/s toward the screen. **Question:** At what time will there first be a focused image on the screen? Enter a number measured in seconds. **Analysis:** 1. **Lens Placement:** - Nearest lens is 45.0 cm from the object. - Second lens is initially 5.00 cm further from the nearest lens. 2. **Movement:** - Second lens moves at 0.5 cm/s towards the screen. **Calculations:** To solve this, you must use lens equations to determine when the image is focused on the screen as the second lens moves. Consider the focal length, distances involved, and the rate of movement to determine the time \( t \).
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