Question:
Young's double slit experiment setup is in such a way that, when path difference is $\lambda$, then intensity at a point is I. If the path difference is $\lambda/4$, then intensity at the same point is:
Young's double slit experiment setup is in such a way that, when path difference is $\lambda$, then intensity at a point is I. If the path difference is $\lambda/4$, then intensity at the same point is:
Show Hint
Intensity in interference is proportional to the square of the cosine of half the phase difference.
Updated On: Jun 10, 2026
- $I/\sqrt{2}$
- $I/2$
- $2I$
- $\sqrt{2}I$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Concept
Intensity $I = I_0 \cos^2(\phi/2)$, where phase difference $\phi = (2\pi/\lambda) \Delta x$.
Step 2: Analysis
For path difference $\lambda$, $\phi = 2\pi$, so $I = I_0 \cos^2(\pi) = I_0$. Thus $I_0 = I$. For path difference $\lambda/4$, $\phi = (2\pi/\lambda) \cdot (\lambda/4) = \pi/2$. Intensity $I' = I \cos^2(\pi/4) = I \cdot (1/\sqrt{2})^2 = I/2$.
Step 3: Conclusion
The intensity becomes $I/2$.
Final Answer: (B)
Intensity $I = I_0 \cos^2(\phi/2)$, where phase difference $\phi = (2\pi/\lambda) \Delta x$.
Step 2: Analysis
For path difference $\lambda$, $\phi = 2\pi$, so $I = I_0 \cos^2(\pi) = I_0$. Thus $I_0 = I$. For path difference $\lambda/4$, $\phi = (2\pi/\lambda) \cdot (\lambda/4) = \pi/2$. Intensity $I' = I \cos^2(\pi/4) = I \cdot (1/\sqrt{2})^2 = I/2$.
Step 3: Conclusion
The intensity becomes $I/2$.
Final Answer: (B)
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Youngs double slit experiment Questions
- A metal wire with circular cross section and length one metre is pulled with tensile force of 1000 N on each side. For the wire to be stretched not more than 0.25 cm, the minimum diameter of the wire required is:
(Young's modulus of the metal $= 10^{11}$ \text{ Pa, take } $\sqrt{\pi} = 1.77$) - In a Young’s double slit experiment, a laser light of wavelength 560 nm produces an interference pattern with consecutive bright fringes’ separation of 7.2 mm. Now another light is used to produce an interference pattern with consecutive bright fringes’ separation of 8.1 mm. The wavelength of the second light is:
- In a Young's double slit experiment, if the wavelength of light is increased by 50% and the distance between the slits is doubled, then the percentage change in fringe width is:
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions