The ratio of resolving powers of an optical microscope for two wavelengths λ _1=4000 Å and λ _2=6000 Å is

Two thin lenses of focal lengths f₁ = +20 cm and f₂ = -10 cm are in contact. The power of the combination is:

The refractive index of glass is 1.5. The speed of light in glass is:

In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power $(p)$ and magnification $(m)$ for each lens will be, respectively

A microscope has an objective of focal length 2 cm , eyepiece of focal length 4 cm and the tube length of 40 cm . If the distance of distinct vision of eye is 25 cm , the magnification in the microscope is :

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at $22.5^{\circ}$ from the polarization axis of one of the polaroid, is ( $\mathrm{I}_0$ is the intensity of polarised light after passing through the first polaroid):