What is the focal length of a lens that forms a virtual image at a distance of 2

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Question: What is the focal length of a lens that forms a virtual image at a distance of 20 cm when the object is placed at 10 cm?

Options:

Correct Answer: 5 cm

Solution:

Using the lens formula, 1/f = 1/v - 1/u. Here, v = -20 cm (virtual image), u = -10 cm. Solving gives f = 5 cm.

What is the focal length of a lens that forms a virtual image at a distance of 20 cm when the object is placed at 10 cm?

What is the focal length of a lens that forms a virtual image at a distance of 20 cm when the object is placed at 10 cm?

Step 1: Understand the lens formula, which is 1/f = 1/v - 1/u.
Step 2: Identify the values for v and u. The virtual image distance (v) is -20 cm (negative because it's virtual) and the object distance (u) is -10 cm (negative because it's on the same side as the object).
Step 3: Substitute the values into the lens formula: 1/f = 1/(-20) - 1/(-10).
Step 4: Calculate 1/(-20) which is -0.05 and 1/(-10) which is -0.1.
Step 5: Now, substitute these values: 1/f = -0.05 - (-0.1).
Step 6: Simplify the equation: 1/f = -0.05 + 0.1 = 0.05.
Step 7: To find f, take the reciprocal: f = 1/0.05.
Step 8: Calculate f, which gives f = 20 cm.

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