Advertisements
Advertisements
Question
Define the critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.
Solution
The angle of incidence corresponding to an angle of refraction of 90° is called the critical angle for the given pair of media. If the angle of incidence of light, when travelling from a denser medium to a rarer medium, is greater than the critical angle then total internal reflection takes place.
Let the angle of incidence i and C be the critical angle C.
Let the angle of refraction r = 90°.
The refractive index of the rarer medium is μa.
The refractive index of the denser medium is μb.
Applying Snell's law,
`(sini)/(sinr) = mu_a/mu_b`
μb sinC = μa sin90° ....[∵ i = C and r = 90°]
`mu_a/mu_b = 1/(sinC)`
Thus, we arrive at a formula expressing the critical angle and refractive index relation:
`""_amu_b = 1/(sinC)`
APPEARS IN
RELATED QUESTIONS
What type of wavefront will emerge from a (i) point source, and (ii) distance light source?
A point source of light is placed at a distance of 2 f from a converging lens of focal length f. The intensity on the other side of the lens is maximum at a distance
A convex lens has a focal length of 10 cm. Find the location and nature of the image if a point object is placed on the principal axis at a distance of (a) 9.8 cm, (b) 10.2 cm from the lens.
An extended object is placed at a distance of 5.0 cm from a convex lens of focal length 8.0 cm. (a) Draw the ray diagram (to the scale) to locate the image and from this, measure the distance of the image from the lens. (b) Find the position of the image from the lens formula and see how close the drawing is to the correct result.
A 5 mm high pin is placed at a distance of 15 cm from a convex lens of focal length 10 cm. A second lens of focal length 5 cm is placed 40 cm from the first lens and 55 cm from the pin. Find (a) the position of the final image, (b) its nature and (c) its size.
A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.
Two convex lenses, each of focal length 10 cm, are placed at a separation of 15 cm with their principal axes coinciding. (a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c) Find the focal length of the equivalent lens. (Note that the sign of the focal length is positive although the lens system actually diverges a parallel beam incident on it.)
According to new Cartesian sign conventions, all the distances are measured from the ______.
A spherical surface of radius R separates two medium of refractive indices µ1 and µ2, as shown in figure. Where should an object be placed in the medium 1 so that a real image is formed in medium 2 at the same distance?
A ray of light from a denser medium strikes a rarer medium at an angle of incidence i as shown in the figure. Refracted and reflected rays make an angle of 90° with each other. The angle of reflection and refraction are r and r'. The critical angle is ______.
