What is the focal length of a concave mirror if an object is placed at a distance of 30 cm from the mirror and the image is formed at a distance of 15 cm from the mirror?
Practice Questions
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Q1
What is the focal length of a concave mirror if an object is placed at a distance of 30 cm from the mirror and the image is formed at a distance of 15 cm from the mirror?
10 cm
15 cm
20 cm
25 cm
Using the mirror formula, 1/f = 1/v + 1/u. Here, v = -15 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = -10 cm.
Questions & Step-by-step Solutions
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Q
Q: What is the focal length of a concave mirror if an object is placed at a distance of 30 cm from the mirror and the image is formed at a distance of 15 cm from the mirror?
Solution: Using the mirror formula, 1/f = 1/v + 1/u. Here, v = -15 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = -10 cm.
Steps: 8
Step 1: Identify the given values. The object distance (u) is -30 cm (negative because it is in front of the mirror) and the image distance (v) is -15 cm (negative because it is a real image formed in front of the mirror).
Step 2: Write down the mirror formula: 1/f = 1/v + 1/u.
Step 3: Substitute the values of v and u 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. Now add the fractions: -2/30 + -1/30 = -3/30.
Step 7: Simplify -3/30 to -1/10.
Step 8: Now, we have 1/f = -1/10. To find f, take the reciprocal: f = -10 cm.
