Question

An object is placed at a certain distance on the principal axis of a concave mirror. If the image distance (v) is 30 cm and radius of curvature (R) of the mirror is 20 cm, find the object distance (u)

• A. 10 cm
• B. 15 cm
• C. 30 cm
• D. 7.5 cm

Answer 1

The Correct Option is B

To solve the problem, we need to find the object distance \( u \) for a concave mirror using the mirror formula.

1. Mirror Formula:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Where:
\( v = \) image distance = +30 cm (positive for real image on same side as object),
\( R = \) radius of curvature = 20 cm,
\( f = \frac{R}{2} = \frac{20}{2} = 10 \, \text{cm} \Rightarrow f = -10 \, \text{cm} \) (negative for concave mirror)

2. Substituting into Mirror Formula:
\[ \frac{1}{-10} = \frac{1}{30} + \frac{1}{u} \]
Solving for \( \frac{1}{u} \): \[ \frac{1}{u} = \frac{1}{-10} - \frac{1}{30} = \frac{-3 - 1}{30} = \frac{-4}{30} = \frac{-2}{15} \]
\[ u = \frac{-15}{2} = -7.5 \, \text{cm} \]

3. Interpreting the Result:
The negative sign indicates the object is on the same side as the mirror, which is expected for a real object in mirror problems.

Final Answer:
The object distance is 7.5 cm (Option D).