Question

The focal length of a lens is 0.1 m. Then the lens must be :
This question has multiple correct options.
A. Convex
B. Concave
C. Cylindrical
D. None of these

Answer 1

In this type of questions where the type of lens is asked, Use the formula of focal length of lens that is $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$.
Where f is focal length,
u object distance,
v is image distance.
Also, in convex lens, their focal length is positive, always
and of concave lens it is negative.
Now, you can proceed to solve the question.

Complete step by step answer:
As the focal length of a lens is positive it can both be convex or cylindrical lens because of a convex lens converges parallel rays to a focal point with a positive focal length because light goes through lens, positive image distances and real images, are on the opposite side of the lens from the object image will be inverted relative to actual image.
Whereas, A concave lens diverges parallel rays away from a focal point has negative focal length and forms only virtual. Smaller images, negative image distance from virtual images on the same side of the lens as the object. The image will be oriented the same direction as the original image just smaller.
Now,
To find the focal length of a lens, measure the distance and plug the numbers in to the focal length formula. Be sure all measurements use the same measurement system.
Then.
Focal length, formula shown below :
$\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$
Where,
f = focal length of a lens
u = distance from the original object to the lens
v = distance from the lens to the image
Hence, the convex lens or cylindrical lens, focal length is positive. Answer i.e., (A) & (C).

Note: In this type of question where the type of lens is asked, we need to first know the kind of focal length a convex lens and a concave lens has then only we will be able to know the answer to this type of question. Also, we need to know about the signs while using the formula for lens or magnification (i.e. $m = \dfrac{V}{U}$), the answer will go wrong totally without the proper signs that are negative and positive. So, keeping in mind the formula and signs proceed to solve this type of question.