Question

What is the type of a lens of Power $$=-4D$$
(A) Convex lens
(B) Concavo Convex lens
(C) Concave lens
(D) None

Answer 1

Hint: Power of a lens is the measure of the amount of deviation of ray of light that can be produced by the lens. Mathematically, it is calculated as the inverse of the focal length of the lens. Using these , find out what type of lens has a negative focal length and justify your answer.

Complete Step by Step solution:
The power of the lens is given as$$-4D$$. As defined, power of lens is the measure of deviation of a light ray that can be done by the lens. It is generally measured in Dioptre. Now , the given power of the lens is said to be negative, let’s find the focal length of the lens using the formula,
$$\Rightarrow P={\displaystyle \frac{1}{f}}$$
Where, $$f$$is the focal length of the lens
Substituting the values we get,
$$\Rightarrow f={\displaystyle \frac{1}{-4}}$$
$$\Rightarrow f={\displaystyle \frac{-100}{4}}$$
$$\Rightarrow f=-25cm$$
Now, let us take a look at the options,
A convex lens, or the converging lens, converges the ray of light from one end to the screen on the other side of the mirror. So the light rays are said to fall on the screen that is on the other side of the lens, which means that the focal length of the mirror is on the positive x-axis plane. Hence, the power of convex lens is always positive.
A concave lens , or the diverging lens , diverges the light rays away from the mirror , and there’s a possibility that the light rays won’t even meet on the other side. There will be a highly diminished virtual image formed near the lens , which is said to be the meeting point of the light rays.
The image and the object are said to be in same side, hence the focal length is on the negative x- axis

Hence, the given lens is concave and option(c) is the right answer.

Note: Concavo-Convex lenses are a type of lens where one side of the mirror is concave and the other side is purely convex. In these types of mirrors, the concave face has a greater degree of curvature and radius of curvature than the convex face.