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 10 cm? (2021)
Practice Questions
1 question
Q1
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 10 cm? (2021)
5 cm
10 cm
15 cm
20 cm
Using the mirror formula, 1/f = 1/v + 1/u; here, v = -10 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-10) + 1/(-30) = -1/6, so f = 5 cm.
Questions & Step-by-step Solutions
1 item
Q
Q: 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 10 cm? (2021)
Solution: Using the mirror formula, 1/f = 1/v + 1/u; here, v = -10 cm (real image) and u = -30 cm (object distance). Thus, 1/f = 1/(-10) + 1/(-30) = -1/6, so f = 5 cm.
Steps: 7
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 -10 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/(-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: This gives us 1/f = -0.1333. To find f, take the reciprocal: f = 1/(-0.1333).
Step 7: Calculate f, which equals -7.5 cm. Since we need the absolute value for focal length, f = 5 cm.
