Question

With the object located a distance of 10 cm from the lens, you measure that the magnitude of the magnification of a well-focused image is 2. How far must the screen be located from the lens to create this well-focused image?

a) 5 cm
b) 20 cm
c) 15 cm
d) 40 cm

Answer 1

To create a well-focused image with a magnification of 2, the screen must be located 20 cm from the lens.

Step-by-step explanation:

To find the distance at which the screen must be located to create a well-focused image with a magnification of 2, we can use the lens formula:

1/f = 1/do + 1/di

Here, f is the focal length of the lens, do is the object distance, and di is the image distance.

Given that the object is located 10 cm from the lens and the magnification is 2, we can use the magnification formula:

magnification = -di/do

Let's substitute the values and solve:

Focusing on the second equation, we have:

2 = -di/10

Solving for di, we get:

di = -20 cm

Since the image distance is negative, the image is virtual. To find the distance at which the screen must be located, we can use the lens formula:

1/f = 1/do + 1/di

Substituting the values, we get:

1/f = 1/10 + 1/-20

1/f = 1/10 - 1/20

1/f = 2/20 - 1/20

1/f = 1/20

Therefore, the screen must be located at a distance of 20 cm from the lens to create this well-focused image.