Question

Find the location of image after reflection from concave mirror.

• A. 30 cm to left of P1
• B. 30 cm to left of P2
• C. 30 cm right to P1
• D. 30 cm right to P2

Answer 1

Answer: (A)

30 cm to left of P1

Answer 2

1. Identify the given parameters for the concave mirror:

• The object is placed in front of the concave mirror.
• Radius of curvature of the concave mirror, $R = 20$ cm.
• Focal length of the concave mirror, $f = \frac{R}{2} = \frac{20}{2} = 10$ cm. Since it is a concave mirror, according to the sign convention (light travels from left to right, and the mirror pole P1 is the origin), the focal length is negative: $f = -10$ cm.
• Object distance from the concave mirror, $u = 15$ cm. Since the object is placed to the left of the concave mirror (P1), according to the sign convention, the object distance is negative: $u = -15$ cm.

2. Apply the mirror formula:

The mirror formula is given by: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

Substitute the values of $f$ and $u$: $\frac{1}{-10} = \frac{1}{v} + \frac{1}{-15}$

Rearrange the equation to solve for $v$: $\frac{1}{v} = \frac{1}{-10} - \frac{1}{-15}$ $\frac{1}{v} = -\frac{1}{10} + \frac{1}{15}$

Find a common denominator, which is 30: $\frac{1}{v} = -\frac{3}{30} + \frac{2}{30}$ $\frac{1}{v} = \frac{-3 + 2}{30}$ $\frac{1}{v} = \frac{-1}{30}$

Therefore, $v = -30$ cm.

3. Interpret the result:

The negative sign for $v$ indicates that the image is formed on the same side as the object (in front of the mirror, which is to the left of P1). The magnitude of $v$ is 30 cm. So, the image is formed 30 cm to the left of the concave mirror (P1).