What is the focal length of a concave lens if it forms a virtual image at a distance of 20 cm from the lens?
Practice Questions
1 question
Q1
What is the focal length of a concave lens if it forms a virtual image at a distance of 20 cm from the lens?
-10 cm
-20 cm
10 cm
20 cm
For a concave lens, the focal length (f) is negative. The virtual image distance (v) is -20 cm. Using the lens formula 1/f = 1/v + 1/u, we can find f. Since v = -20 cm, we can assume u is at infinity, thus 1/f = 1/(-20) + 0, giving f = -20 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the focal length of a concave lens if it forms a virtual image at a distance of 20 cm from the lens?
Solution: For a concave lens, the focal length (f) is negative. The virtual image distance (v) is -20 cm. Using the lens formula 1/f = 1/v + 1/u, we can find f. Since v = -20 cm, we can assume u is at infinity, thus 1/f = 1/(-20) + 0, giving f = -20 cm.
Steps: 8
Step 1: Understand that a concave lens always forms a virtual image.
Step 2: Know that for a concave lens, the focal length (f) is negative.
Step 3: Identify the distance of the virtual image (v) from the lens, which is given as 20 cm. Since it's a virtual image, we write v as -20 cm.
Step 4: Use the lens formula: 1/f = 1/v + 1/u. Here, u is the object distance.
Step 5: Assume the object is at infinity, which means u is very large. In this case, 1/u approaches 0.
Step 6: Substitute the values into the lens formula: 1/f = 1/(-20) + 0.
Step 7: Simplify the equation: 1/f = -1/20.
Step 8: Invert the equation to find f: f = -20 cm.
