JEE

The compound microscope comprises two convex lenses - the eyepiece (lower power) and the objective (high power, short focal length). The objective forms a magnified, inverted, and real image of a small object placed just beyond its focal point. Magnifying power is M = (L/f? ) * (D/f? ), where f? is the objective's focal length, L is the tube length, and f? is the eyepiece's focal length. This image acts as the object for the eyepiece.

The formula says that for a thin lens, the focal length (f) to its refractive index (? ) and radii of curvature (R? , R? ). Let a thin lens with surfaces of radii R? (first surface) and R? (second surface). We can use the refraction formula to calculate the image formation by the first surface. Following is the formula -? /v -? /u = (? -? )/R. Then we can combine both refractions and assume a lens in air (? = 1).

For mirrors and lenses, the Cartesian sign convention is used. For lenses: For convex lenses, the focal length is positive and for concave lenses, it is negative. Distances to the right of the optical center are positive.
For mirrors: For concave mirrors, the focal length is positive and for convex, it is negative. The distances to the right of the optical center are positive. The sign convention allows for consistent calculations for formulas like mirror and lens formulas, and for ray diagrams.

Diffraction leads to the formation of patterns of varying intensity. When around obstacles, waves bend and spread through the narrow opening, it is called diffraction. The interference results in a new wave pattern and involves the superposition of two or more coherent waves. Both these phenomena produce patterns of light and dark regions; the interference results from the combination of multiple waves and the diffraction arises from a single wave interacting with an aperture or obstacle. When the size of the aperture or obstacle is comparable to the wavelength of the wave, diffraction patterns are typically observed.

A coherent light source in Young's Double Slit Experiment illuminates two closely spaced slits, and produces two overlapping light waves. The interference of these waves constructively or destructively based on their phase difference lead to a pattern of bright and dark fringes on a screen, When the path difference is an integral multiple of the wavelength, it is constructive interference (bright fringes) and when the path difference is an odd multiple of half the wavelength, it is destructive interference (dark fringes). Through observable interference patterns, Young's Double Slit Experiment, shows the wave nature of light.