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.