If the focal length of a lens is doubled, how does the power of the lens change?

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Question: If the focal length of a lens is doubled, how does the power of the lens change?

Options:

Correct Answer: Halves

Solution:

Power is inversely proportional to focal length. If f is doubled, P = 1/f will halve.

If the focal length of a lens is doubled, how does the power of the lens change?

If the focal length of a lens is doubled, how does the power of the lens change?

Step 1: Understand that the power of a lens (P) is calculated using the formula P = 1/f, where f is the focal length of the lens.
Step 2: Recognize that if the focal length (f) is doubled, it means the new focal length is 2f.
Step 3: Substitute the new focal length into the power formula: P = 1/(2f).
Step 4: Compare the new power (P = 1/(2f)) with the original power (P = 1/f).
Step 5: Notice that 1/(2f) is half of 1/f, which means the new power is half of the original power.
Step 6: Conclude that if the focal length is doubled, the power of the lens is halved.

Lens Power and Focal Length – The power of a lens is defined as the inverse of its focal length (P = 1/f), meaning that as the focal length increases, the power decreases.