If focal length of a concave lens is 50 cm, then the power of the lens would be

The correct answer is -2 D.

Step-by-step Explanation:

1. Identify the type of lens and its sign convention:
The given lens is a concave lens. By convention, the focal length of a concave lens is negative.

Therefore, we can write:
$$f=-50\text{ cm}$$

2. Convert the focal length from centimeters to meters:
To calculate the power, the focal length must be expressed in meters (m):
$$f=\frac{-50}{100}\text{ m}$$

Which simplifies to:
$$f=-0.5\text{ m}$$

3. Use the formula for the power of a lens:
The power of a lens is the reciprocal of its focal length when measured in meters:
$$P=\frac{1}{f\text{ (in meters)}}$$

Substituting the value of the focal length into the formula:
$$P=\frac{1}{-0.5\text{ m}}$$

This gives:
$$P=-2\text{ D}$$
(where D stands for dioptre, the SI unit of lens power).

Hence, the power of the concave lens is -2 D.