Definitions [1]
What is a Polaroid?
A Polaroid is a material which polarises light. The phenomenon of selective absorption is made use of in the construction of polariods. There are different types of polaroids.
A Polaroid consists of micro crystals of herapathite (an iodosulphate of quinine). Each crystal is a doubly refracting medium, which absorbs the ordinary ray and transmits only the extra ordinary ray. The modern polaroid consists of a large number of ultra microscopic crystals of herapathite embedded with their optic axes, parallel, in a matrix of nitro - cellulose.
Recently, new types of polariod are prepared in which thin film of polyvinyl alcohol is used. These are colourless crystals which transmit more light, and give better polarisation.
Theorems and Laws [1]
Prove that the frequency of beats is equal to the difference between the frequencies of the two sound notes giving rise to beats.
Consider two sound waves, having the same amplitude and slightly different frequencies n1 and n2. Let us assume that they arrive in phase at some point x of the medium. The displacement due to each wave at any instant of time at that point is given as
`y_1 = A sin {2pi (n_1t - x/lambda_1)}`
`y_2 = A sin {2pi (n_2t - x/lambda_2)}`
Let us assume for simplicity that the listener is at x = 0.
∴ y1 = A sin (2πn1t) ...(i)
and y2 = A sin (2πn2t) ...(ii)
According to the principle of superposition of waves,
y = y1 + y2
∴ y = A sin (2πn1t) + A sin (2πn2t)
By using formula,
sin C + sin D = 2 sin `((C + D)/2) cos ((C − D)/2)`
y = `A[2sin((2pin_1t + 2pi n_2t)/2 )] cos [((2pin_1t - 2pin_2t)/2)]`
y = `2A sin [2pi ((n_1 + n_2)/2)t] cos [2pi ((n_1 - n_2)/2)t]`
∴ y = `R sin [2pi ((n_1 + n_2)/2)t]`
y = R sin (2πnt) ...(iii)
Where,
R = `2A cos[(2pi(n_1 - n_2))/(2)t]` and n = `(n_1 + n_2)/2`
Equation (iii) is the equation of a progressive wave having frequency `((n_1 + n_2)/2)` and resultant amplitude R.
For waxing,
A = ± 2a
`therefore 2A cos [2pi((n_1 - n_2)/2)t] = +- 2A`
`therefore cos [2pi ((n_1 - n_2)/2)]t = +-( 2A)/(2A)`
`therefore cos [2pi ((n_1 - n_2)/2)]t = +- 1`
This is possible if
`2pi ((n_1 - n_2)/2)t = 0, pi, 2pi, 3pi, ....`
i.e. t = 0, `1/(n_1 - n_2), 2/(n_1 - n_2), 3/(n_1 - n_2), ...`
∴ Period of beat T = `[1/(n_1 - n_2) - 0]`
T = `1/(n_1 - n_2)`
∴ Frequency of beats n = `1/T`
n = n1 − n2
Thus, the frequency of beats is equal to the difference between the frequencies of the two sound notes giving rise to beats.
Important Questions [27]
- Determine the Change in Wavelenght of Light During Its Passage from Air to Glass, If the Refracrtive Index of Glass with Respect to Air is 1.5 and the Frequency of Light is 5 X 1014 Hz. Find the Wave Number of Light in Glass (Velocity of Light in Air
- The Minimum Angular Separation Between Two Stars is 4 × 10−6 Rad, If Telescope is Used to Observe Them with an Objective of Aperture 16 Cm. Find the Wavelength of Light Used.
- Explain the Construction of Plane Wavefront Using Huygens’ Principle.
- The Refractive Indices of Water and Diamond Are `4/3` and 2.42 Respectively. Find the Speed of Light in Water and Diamond. (C = 3x108 M/S)
- On the Basis of Huygens' Wave Theory of Light Prove That Velocity of Light in a Rarer Medium is Greater than Velocity Of Light in a Denser Medium.
- Determine the change in wavelength of light during its passage from air to glass. If the refractive index of glass with respect to air is 1.5 and the frequency of light is 3.5 x 1014 Hz
- Explain Refraction of Light on the Basis of Wave Theory. Hence Prove the Laws of Refraction
- Define Polarisation in Dielectrics.
- The Refractive Indices of Glass and Water W.R.T. Air Are 3/2 And 4/3 Respectively. Determine The Refractive Index of Glass W.R.T. Water.
- Draw a Neat Labelled Diagram Showing the Plane of Vibration and Plane of Polarisation for Polarised Light.
- The Refractive Indices of Water for Red and Violet Colours Are 1.325 and 1.334 Respectively. Find the Difference Between the Velocities of Rays for These Two Colours in Water.
- A Ray of Light Passes from a Vacuum to a Medium of Refractive Index (μ). the Angle of Incidence is Found to Be Twice the Angle of Refraction. the Angle of Incidence is
- State Two Uses of Polaroid.
- The Glass Plate of Refractive Index 1.732 is to Be Used as a Polarizer, Its Polarising Angle is _______.
- For a Glass Plate as a Polariser with Refractive Index 1.633, Calculate the Angle of Incidence at Which Light is Polarised.
- What is the Refractive Index of the Medium, If the Polarising Angle for a Given Medium is 60°
- If the critical angle of a medium is sin-1(3/5), find the polarising angle.
- What is a Polaroid?
- State Brewster’s law and show that when light is incident at polarizing angle the reflected and refracted rays are mutually perpendicular to each other.
- Two tuning forks of frequencies 320 Hz and 340 Hz are sounded together to produce a sound wave. The velocity of sound in air is 326.4 m/s. Calculate the difference in wavelengths of these waves.
- Find the Velocity of Sound in the Air and Frequency of the Tuning Fork
- In Doppler Effect of Light, the Term “Red Shift” is Used for
- Doppler Effect is Not Applicable When
- The Working of Radar is Based on
- Apparent Frequency of the Sound Heard by a Listener is Less than the Actual Frequency of Sound Emitted by Source. in this Case
- State Any Four Applications Of Doppler Effect
- Prove that the frequency of beats is equal to the difference between the frequencies of the two sound notes giving rise to beats.
