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Ray Optics And Optical Instruments

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Total internal reflection in a prism

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Some cases of total internal reflection in a prism are discussed below:

1. Right-angled isosceles prism/Total reflecting prism():
Light ray incident normally on a smaller side is deviated by .
Light ray incident normally on hypotenuse is deviated by .
Erecting prism: When object placed at an angle to the smaller side in front of the smaller side, its image is inverted on the other side. 
2. Equilateral prism(): Light incident normally on a side undergoes total internal reflection on other side. Angle of deviation is .
3. Right angled prism():
Light ray incident normally on the smallest side undergoes total internal reflection at hypotenuse.
Light ray incident normally on the longer side (not hypotenuse) does not undergo total internal reflection.
Light ray incident normally on the hypotenuse may or may not undergo total-internal reflection depending upon the point of entering the prism. 
Two monochromatic rays of light are incident normally on the face AB of a isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.35 and 1.45. Trace the path of these rays after entering through the prism.

Lens Maker's Formula

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Consider a convex lens (or concave lens) of absolute refractive index  to be placed in a rarer medium of absolute refractive index . Considering the refraction of a point object on the surface , the image is formed at  who is at a distance of .

 (as the lens is thin)

It follows from the refraction due to convex spherical surface

The refracted ray from A suffers a second refraction on the surface and emerges along BI. Therefore I is the final real image of O.

Here the object distance is

is very small


(Final image distance)

Let  be radius of curvature of second surface of the lens. It follows from refraction due to concave spherical surface from denser to rarer medium that



But and

Thus we get=

Derive the Lens Maker's formula.

Image formation when multiple lenses are used

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What should be the value of distance so that final image is formed on the object itself? (Focal lengths of the lenses are written on the lenses.)
Image after refraction from first lens:
Image after second refraction from concave lens,
or, (If final image is formed on object itself)
Three lenses of focal length and are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.


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Telescope is an optical device used to form the image of very far objects near the eye so that it appears bigger. It is hence used to obtain angular magnification. It is used to study the astronomical objects.  It consists of two convex lenses. Image formed by objective lens is real and inverted and is formed at its focal point. It is large in size to capture more light and improve magnification. Image formed by objective lens serves as the object for eyepiece lens.  Image formed by eyepiece lens is virtual and erect. 
Describe the astronomical telescope on the basis of the following points:
(i) Labelled Ray diagram.
(ii) Derivation of formula for magnifying power, when final image is formed at the least distance of distinct vision.

You are given following three lenses. Which two lenses will you see as an eyepiece and as an objective to construct an astronomical telescope?