$A$ screen is placed $90\, cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20\, cm$. The focal length of the lens is.....$ cm$

$A$ convex lens makes a real image $4 \, cm$ long on a screen. When the lens is shifted to a new position without disturbing the object,we again get a real image on the screen which is $16 \, cm$ tall. The length of the object must be.......$cm$

$A$ magnifying glass is to be used at a fixed object distance of $1 \text{ inch}$. If it is to produce an erect image magnified $5$ times,its focal length should be ........ $\text{inch}$.

When will the convergent nature of a convex lens be less as compared to its nature in air?

$A$ convex lens is made of glass $(\mu_g = 1.5)$ and has a focal length of $4 \, cm$ in air. If it is immersed in water $(\mu_w = 1.33)$,what will be its new focal length in $cm$?

The optical power of a thin glass lens (refractive index $1.5$) in air is $-5 \ D$. What will be its optical power in a liquid with a refractive index of $1.6$ (in $D$)?