What is the focal length of a concave mirror if an object placed at a distance o

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Question: What is the focal length of a concave mirror if an object placed at a distance of 30 cm produces an image at a distance of 15 cm?

Options:

Correct Answer: 10 cm

Solution:

Using the mirror formula, 1/f = 1/v + 1/u; here, v = -15 cm (real image) and u = -30 cm. Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = 10 cm.

What is the focal length of a concave mirror if an object placed at a distance of 30 cm produces an image at a distance of 15 cm?

What is the focal length of a concave mirror if an object placed at a distance of 30 cm produces an image at a distance of 15 cm?

Step 1: Identify the given values. The object distance (u) is -30 cm (negative because it's in front of the mirror) and the image distance (v) is -15 cm (negative because it's a real image).
Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values into the formula: 1/f = 1/(-15) + 1/(-30).
Step 4: Calculate 1/(-15) which is -1/15 and 1/(-30) which is -1/30.
Step 5: Find a common denominator to add the fractions: The common denominator for 15 and 30 is 30.
Step 6: Rewrite -1/15 as -2/30, so now we have: 1/f = -2/30 + -1/30.
Step 7: Add the fractions: 1/f = -3/30.
Step 8: Simplify -3/30 to -1/10.
Step 9: Take the reciprocal to find the focal length: f = -10 cm.
Step 10: Since the focal length is negative, it confirms that it is a concave mirror.

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