Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
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
संबंधित प्रश्न
What type of wavefront will emerge from a (i) point source, and (ii) distance light source?
The equation of refraction at a spherical surface is \[\frac{\mu_2}{\nu} - \frac{\mu_1}{\mu} = \frac{\mu_2 - \mu_1}{R}\]
Taking \[R = \infty\] show that this equation leads to the equation
\[\frac{\text{ Real depth }}{\text{ Apparent depth }} = \frac{\mu_2}{\mu_1}\]
for refraction at a plane surface.
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.
A slide projector has to project a 35 mm slide (35 mm × 23 mm) on a 2 m × 2 m screen at a distance of 10 m from the lens. What should be the focal length of the lens in the projector?
A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.
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.
Define the term ‘focal length of a mirror’.
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 ______.
A point object in the air is placed symmetrically at a distance of 60 cm in front of a concave spherical surface with a refractive index of 1.5. If the radius of curvature of the surface is 20 cm, find the position of the image formed.
