An object is placed 60 cm in front of a convex lens with a focal length of 20 cm. Where does the image form?
A. 15 cm
Answer (1)
Start with the lens formula: f 1 = u 1 + v 1 .
Substitute f = 20 cm and u = 60 cm into the formula: 20 1 = 60 1 + v 1 .
Solve for v : v 1 = 20 1 − 60 1 = 30 1 .
Find the image distance: v = 30 cm .
Explanation
Problem Analysis and Given Data We are given the object distance u = 60 cm and the focal length of a convex lens f = 20 cm. We need to find the image distance v .
Lens Formula We will use the lens formula to find the image distance: f 1 = u 1 + v 1 where f is the focal length, u is the object distance, and v is the image distance.
Substitution Substitute the given values into the lens formula: 20 1 = 60 1 + v 1 Now, we need to solve for v .
Solving for v Rearrange the equation to isolate v 1 :
v 1 = 20 1 − 60 1 Find a common denominator, which is 60: v 1 = 60 3 − 60 1 v 1 = 60 2 v 1 = 30 1
Final Calculation Now, take the reciprocal of both sides to find v :
v = 30 So, the image distance is 30 cm.
Examples
Understanding lenses helps us design better cameras and telescopes. For example, if you're designing a camera and need to focus an image sharply on the sensor, you need to know the lens's focal length and the distance to the object you're photographing. Using the lens formula, you can calculate where the image will form and adjust the lens position accordingly to get a clear picture. This principle is also crucial in designing eyeglasses to correct vision problems.
