Focal length of a concave mirror ‘f’ can be computed as _______ where u = distance of object needle from pole of the mirror v = distance of image needle from the pole of the mirror
- Auv / (u+v)Correct
- B(uv+1) / (u+v)
- Cuv / (u-v)
- D(uv+1) / (u-v)
Solution
Concept
The focal length of a mirror is the distance from its pole to its focus. We use the mirror formula to find the relationship between focal length, object distance, and image distance.
Formula
1/f = 1/v + 1/u
Step-by-step solution
1. Let 'u' be the distance of the object needle from the pole of the mirror. 2. Let 'v' be the distance of the image needle from the pole of the mirror. 3. Let 'f' be the focal length of the concave mirror. 4. According to the mirror formula: 1/f = 1/v + 1/u. 5. To find 'f', we take the LCM (Least Common Multiple) of the right side: 1/f = (u + v) / (uv). 6. Now, flip both sides to get 'f' alone: f = uv / (u + v). Answer: (A) uv / (u+v)
Explanation
The mirror formula relates the object distance, image distance, and focal length. By solving this equation for 'f', we get the product of distances divided by their sum. This is a standard formula used in physics and surveying optics.
Why the other options are wrong
B: This includes an extra '+1' which is mathematically incorrect for the mirror formula. C: This uses a minus sign, which is the formula for a lens, not a mirror. D: This is mathematically incorrect and uses the wrong sign.
Shortcut
Think of it like resistors in parallel: the combined value is (Product / Sum).
Common mistake
Students often confuse the mirror formula (plus sign) with the lens formula (minus sign).
Correct answer: A) uv / (u+v)