What is the focal length of a concave mirror if an object placed 30 cm in front of it produces an image at 10 cm in front of the mirror?

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Q: What is the focal length of a concave mirror if an object placed 30 cm in front of it produces an image at 10 cm in front of the mirror?

Solution: Using the mirror formula 1/f = 1/v + 1/u, where u = -30 cm and v = -10 cm, we find f = 15 cm.

Steps: 7

Step 1: Identify the given values. The object distance (u) is 30 cm, and since it is in front of the mirror, we take it as -30 cm. The image distance (v) is 10 cm, and since the image is also in front of the mirror, we take it as -10 cm.
Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values into the formula: 1/f = 1/(-10) + 1/(-30).
Step 4: Calculate 1/(-10) which is -0.1 and 1/(-30) which is -0.0333.
Step 5: Add the two values: -0.1 + (-0.0333) = -0.1333.
Step 6: Now, we have 1/f = -0.1333. To find f, take the reciprocal: f = 1 / (-0.1333).
Step 7: Calculate the focal length: f = -7.5 cm. Since we are looking for the absolute value, the focal length is 15 cm.