Young's double slit experiment is performed with monochromatic light of wavelength \( 6000 \text{Ã…} \). If the intensity of light at a point on the screen where the path difference is \( 2000 \text{Ã…} \) is \( I_1 \) and the intensity of light at a point where path difference is \( 1000 \text{Ã…} \) is \( I_2 \), then the ratio \( I_1: I_2 \) is:
Young's double slit experiment is performed with monochromatic light of wavelength \( 6000 \text{Ã…} \). If the intensity of light at a point on the screen where the path difference is \( 2000 \text{Ã…} \) is \( I_1 \) and the intensity of light at a point where path difference is \( 1000 \text{Ã…} \) is \( I_2 \), then the ratio \( I_1: I_2 \) is:
Show Hint
- \( 1:3 \)
- \( 2:1 \)
- \( 1:1 \)
- \( 4:5 \)
The Correct Option is A
Solution and Explanation
To determine the ratio \( I_1 : I_2 \) in Young's double slit experiment, we need to analyze the interference pattern and how the path difference affects the intensity of light at different points on the screen. 1. Given Data: - Wavelength of light, \( \lambda = 6000 \text{Ã…} \) - Path difference at point 1, \( \Delta_1 = 2000 \text{Ã…} \) - Path difference at point 2, \( \Delta_2 = 1000 \text{Ã…} \) - Intensity at point 1, \( I_1 \) - Intensity at point 2, \( I_2 \) 2. Calculate the Phase Difference: - The phase difference \( \phi \) is related to the path difference \( \Delta \) by: \[ \phi = \frac{2\pi \Delta}{\lambda} \] - For point 1: \[ \phi_1 = \frac{2\pi \times 2000 \text{Ã…}}{6000 \text{Ã…}} = \frac{2\pi}{3} \] - For point 2: \[ \phi_2 = \frac{2\pi \times 1000 \text{Ã…}}{6000 \text{Ã…}} = \frac{\pi}{3} \] 3. Calculate the Intensity: - The intensity \( I \) at a point on the screen is given by: \[ I = 4I_0 \cos^2\left(\frac{\phi}{2}\right) \] where \( I_0 \) is the intensity of light from a single slit. - For point 1: \[ I_1 = 4I_0 \cos^2\left(\frac{\phi_1}{2}\right) = 4I_0 \cos^2\left(\frac{\pi}{3}\right) = 4I_0 \left(\frac{1}{2}\right)^2 = I_0 \] - For point 2: \[ I_2 = 4I_0 \cos^2\left(\frac{\phi_2}{2}\right) = 4I_0 \cos^2\left(\frac{\pi}{6}\right) = 4I_0 \left(\frac{\sqrt{3}}{2}\right)^2 = 3I_0 \] 4. Determine the Ratio \( I_1 : I_2 \): - The ratio of the intensities is: \[ I_1 : I_2 = I_0 : 3I_0 = 1 : 3 \] 5. Final Answer: - The ratio \( I_1 : I_2 \) is: \[ \boxed{1:3} \] This corresponds to option (1).
Top TS EAMCET Physics Questions
- A wooden box lying at rest on an inclined surface of a wet wood is held at static equilibrium by a constant force $F$ applied perpendicular to the incline. If the mass of the box is $1\,kg$, the angle of inclination is $30^{\circ}$ and the coefficient of static friction between the box and the inclined plane is $0.2$, the minimum magnitude of $\vec{F}$ is (Use $ g = 10\,m/s^2$)
- A metre scale made of steel reads accurately at $25^{\circ} C$ . Suppose in an experiment an accuracy of $0.06\, mm$ in $1\,m$ is required, the range of temperature in which the experiment can be performed with this metre scale is (coefficient of linear expansion of steel is $ 11 \times 10^{-6} /^{\circ} \, C$ )
- Consider a solenoid carrying current supplied by a DC source with a constant emf containing iron core inside it. When the core is pulled out of the solenoid, the change in current will
- A parallel beam of light of intensity \(I_0\) is incident on a coated glass plate. If \(25\%\) of the incident light is reflected from the upper surface and \(50\%\) of light is reflected from the lower surface of the glass plate, the ratio of maximum to minimum intensity in the interference region of the reflected light is
- A thermocol box has a total wall area (including the lid) of $1.0 m ^{2}$ and wall thickness of $3 cm$. It is filled with ice at $0^{\circ} C$. If the average temperature outside the box is $30^{\circ} C$ throughout the day, the amount of ice that melts in one day is [Use $K_{\text {thermocol }}=0.03 W / mK$ $.L_{\text {fusion (ice) }}=3.00 \times 10^{5} J / kg ]$
Top TS EAMCET Wave optics Questions
N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in a vessel which is maintained at a temperature T. The mean square velocity of the molecules of gas B is denoted by V22 and the mean square of the x-component velocity of the molecules of gas B is denoted by V12, then V1\V2 is:
Among the following statements, the correct statement for a wave is:
Which of the following statements is true about LEDs
- When unpolarized light incident from air on another medium at an angle of 60°, the reflected light is completely polarized. The refractive index of the medium is:
- A car travelling at a speed of \(54 \, \text{kmph}\) towards a wall sounds a horn of frequency \(400 \, \text{Hz}\). The difference in the frequencies of two sounds, one received directly from the car and the other reflected from the wall, noticed by a person standing between the car and the wall is: (Speed of sound in air is \(335 \, \text{m/s}\))
Top TS EAMCET Questions
- A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
- If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is
- If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$
- $A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is