An object is located in a fixed position in front of a screen. $A$ sharp image is obtained on the screen for two positions of a thin lens separated by $10\, cm$. The size of the images in the two situations are in the ratio $3 : 2$. What is the distance between the screen and the object in $cm$?

An achromatic combination is made with a lens of focal length $f$ and dispersive power $\omega$ with a lens having a dispersive power of $2\omega$. The focal length of the second lens will be:

Explain the first focal point and second focal point for a lens.

The focal length of a lens with a refractive index of $1.5$ in air is $0.30 \ m$. When it is immersed in a liquid of refractive index $\frac{4}{3}$,its focal length in the liquid will be ...... $cm$.

$A$ thin lens of focal length $f$ and its aperture has a diameter $d$. It forms an image of intensity $I$. Now, the central part of the aperture up to diameter $(d/2)$ is blocked by an opaque paper. The focal length and image intensity would change to:

$A$ thin lens of material having refractive index $\mu = 1.5$ and focal length of $20 \ cm$ in air has two media of different refractive indices $\mu_1 = 1.2$ and $\mu_2 = 2.5$ covering the upper and lower halves of the lens,respectively,as shown in the figure. If an object is placed on the principal axis,then its two images will be formed,one after refraction from the upper part and the other after refraction from the lower part. Considering the object to be at $\infty$,the separation between the two images formed would be ...... $cm$.