What is the magnification produced by a concave mirror if the object is placed a

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Question: What is the magnification produced by a concave mirror if the object is placed at a distance of 15 cm and the focal length is 5 cm?

Options:

Correct Answer: 3

Solution:

Using the mirror formula, 1/f = 1/v + 1/u, we find v = -7.5 cm. Magnification (m) = -v/u = 7.5/15 = 0.5.

What is the magnification produced by a concave mirror if the object is placed at a distance of 15 cm and the focal length is 5 cm?

What is the magnification produced by a concave mirror if the object is placed at a distance of 15 cm and the focal length is 5 cm?

Step 1: Identify the given values. The object distance (u) is -15 cm (negative because it is in front of the mirror) and the focal length (f) is -5 cm (negative for a concave mirror).
Step 2: Use the mirror formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values into the formula: 1/(-5) = 1/v + 1/(-15).
Step 4: Simplify the equation: -1/5 = 1/v - 1/15.
Step 5: Find a common denominator for the right side, which is 15v: -3v/15 = (15 - v)/15.
Step 6: Rearrange the equation to solve for v: -3v = 15 - v.
Step 7: Combine like terms: -3v + v = 15, which gives -2v = 15.
Step 8: Divide both sides by -2 to find v: v = -7.5 cm.
Step 9: Calculate the magnification (m) using the formula: m = -v/u.
Step 10: Substitute the values: m = -(-7.5)/(-15) = 7.5/15.
Step 11: Simplify the magnification: m = 0.5.

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