Question

An object is placed 15 cm in front of a concave mirror of focal length 10 cm. Find the position and nature of the image.

• A. 30 cm behind mirror, virtual and erect
• B. 30 cm in front of mirror, real and inverted
• C. 15 cm behind mirror, virtual
• D. 20 cm in front of mirror, real

Hint:

For concave mirrors: - If \(v\) is negative → image forms in front of mirror (real). - If \(v\) is positive → image forms behind mirror (virtual).

Answer 1

The Correct Option is B

Concept: The mirror formula is: \[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \] where
• \(u\) = object distance
• \(v\) = image distance
• \(f\) = focal length

Step 1: Substitute the given values. For a concave mirror: \[ u = -15 \text{ cm}, \quad f = -10 \text{ cm} \] \[ \frac{1}{v} + \frac{1}{-15} = \frac{1}{-10} \]

Step 2: Solve for \(v\). \[ \frac{1}{v} = -\frac{1}{10} + \frac{1}{15} \] \[ \frac{1}{v} = \frac{-3 + 2}{30} \] \[ \frac{1}{v} = -\frac{1}{30} \] \[ v = -30 \text{ cm} \]

Step 3: Interpret the result. Negative image distance indicates the image forms in front of the mirror. Thus, the image is: \[ \boxed{30 \text{ cm in front of the mirror, real and inverted}} \]