Advertisements
Advertisements
प्रश्न
A jar of height h is filled with a transparent liquid of refractive index µ (Figure). At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmetrically about the centre, the dot is invisible.
Advertisements
उत्तर
In the figure, ray 1 strikes the surface at an angle less than critical angle c and gets refracted in rear medium. Ray 2 strikes the surface making an angle greater than the critical angle and gets internally reflected. The locus of points where ray strikes at critical angle is a circle called circle of illuminance (C.O.I). All light rays striking inside the circle of illuminance get refracted in the rarer medium. If an observer is in the rear medium, he/she will see light coming out only from within the circle of illuminance. If a circular opaque plate covers the circle of illuminance, no light will get refracted in the rarer medium and then the object cannot be seen from the rarer medium.
In figure, O is a small dot at the bottom of the jar. The ray from the dot emerges out of a circular patch of water surface of diameter AB till the angle of incidence for the rays OA and OB exceeds the critical angle (iC).
Rays of light incident at an angle greater than iC, are totally reflected within the water and consequently cannot emerge out of the water surface.
As `sin i_C = 1/mu` ⇒ `tan i_C = 1/sqrt(mu^2 - 1)`
Now, `(d/2)/h = tan i_c`
⇒ `d/2 = h tan i_c = h 1/sqrt(mu^2 - 1)`
⇒ `d = (2h)/sqrt(mu^2 - 1)`
This is the required expression of d.
APPEARS IN
संबंधित प्रश्न
In the given figure PQ and PR are the two light rays emerging from an object P. The ray PQ is refracted as QS.
- State the special name given to the angle of incidence ∠PQN of the ray PQ.
- What is the angle of refraction for the refracted ray QS?
- Name the phenomenon that occurs if the angle of incidence ∠PQN is increased.
- The ray PR suffers partial reflection and refraction on the water-air surface. Give reason.
- Draw in the diagram the refracted ray for the incident ray PR and hence show the position of image of the object P by the letter P’ when seen vertically from above.
State one factor on which a critical angle for a given pair of media depends. The critical angle for the glass-air interface is 45° for the yellow light. Will it be equal to, less than or greater than 45° for (i) red light, (ii) blue light?
How is the critical angle of a material related to its refractive index?
The diagram shows a point source P inside a water container. Three rays A, B, and C starting from P are shown up to the water surface. Show in the diagram the path of these rays after striking the water surface. The critical angle for the water-air pair is 48°.
The adjacent diagram shows two right-angled isosceles prisms A and B. Complete the diagram to show the path of rays P and Q emerging out of the prism B. What principles have you used to complete the diagram?
Answer the following question.
Define the critical angle of incidence and obtain an expression for it.
Answer the following question.
What are the advantages of optical fibre communication over electronic communication?
The angle of minimum deviation produced by a thin glass prism in air is 'δ'. If that prism is immersed in water, the angle of minimum deviation will be ______.
( aμg = refractive index of glass w.r.t, air aμw = refractive index of water w.r.t. air)
A bundle of glass threads, each of which is capable of transmitting messages using light waves is called ______.
The critical angle is defined as the angle of incidence at which the total internal reflection starts to occur.
Optical Fibres are based on the phenomenon of dispersion.
What is the phenomenon used in optical fiber? Explain.
A ray of light passes through a prism of refractive index `sqrt2` as shown in the figure. Find:
- The angle of incidence (∠r2) at face AC.
- The angle of minimum deviation for this prism.
State two differences between normal reflection and total internal reflection.
When a ray of light is refracted from one medium to another, then the wavelength changes from 6000 Å to 4000 Å. The critical angle for the interface will be ______.
