MHT CET · Physics · Wave Optics
In Young' double slit experiment, for the \(n^{\text {th }}\) dark fringe ( \(n=1,2,3\).....) the phase difference of the interfering waves in radian will be
- A \((2 n-1) \pi\)
- B \((2 n+1) \pi\)
- C \(\mathrm{n} \frac{\pi}{2}\)
- D \((2 n-1) \frac{\pi}{2}\)
Answer & Solution
Correct Answer
(B) \((2 n+1) \pi\)
Step-by-step Solution
Detailed explanation
The resultant intensity of the interfering waves is given by,
\(\mathrm{E}^2 \mathrm{E}_1^2+\mathrm{E}_2^2+2 \mathrm{E}_1 \mathrm{E}_2 \cos (\delta)\)
where, \(\delta\) is the phase difference between the waves.
For a dark fringe, \(\mathrm{E}_1=\mathrm{E}_2\) and \(\cos (\delta)=-1\).
Therefore, the phase \(\delta=(2 n+1) \pi\) is an odd multiple of pi.
\(\mathrm{E}^2 \mathrm{E}_1^2+\mathrm{E}_2^2+2 \mathrm{E}_1 \mathrm{E}_2 \cos (\delta)\)
where, \(\delta\) is the phase difference between the waves.
For a dark fringe, \(\mathrm{E}_1=\mathrm{E}_2\) and \(\cos (\delta)=-1\).
Therefore, the phase \(\delta=(2 n+1) \pi\) is an odd multiple of pi.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- An ideal gas taken through a process ABCA as shown in figure. If the net heat supplied to gas in the cycle is 5 J , then the work done by the gas in process from C to A is
MHT CET 2025 Medium - The bob of a simple pendulum performs SHM with period \(T\) in air and with period \(T_1\) in water. Relation between \(T\) and \(T_1\) is (neglect friction due to water, density of the material of the bob is \(\frac{9}{8} \times 10^3 kg / m ^3\), density of water is \(1 g / cc\) )MHT CET 2016 Medium
- There is hole of area 'A' at the bottom of a cylindrical vessel. Water is filled to a height ' \(h\) ' and water flows out in ' \(t\) ' second. If water is filled to a height ' \(4 \mathrm{~h}\) ', it will flow out in time (in second)MHT CET 2023 Medium
- The \(\mathrm{P}-\mathrm{V}\) diagrams for particular gas of different thermodynamic processes are given by
MHT CET 2024 Easy - When one end of a capillary tube is dipped in water, the height of water column is ' \(h\) '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is
(Surface tension of water \(=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}\) )MHT CET 2025 Medium - A point object kept at \(P\) in front of a glass sphere of radius ' \(R\) ' has its image formed at \(Q\) such that \(\mathrm{PO}=\mathrm{QO}\). The refractive index of material of glass sphere is 1.4. The distance PO is equal to
MHT CET 2024 Hard
More PYQs from MHT CET
- What is the number of moles of ' C ' and ' H ' atoms respectively present in n mole molecule represented by following structure ?
MHT CET 2025 Easy - What is change in internal energy if a system gains \(\mathrm{xJ}\) of heat and yJ work is done on it?MHT CET 2022 Easy
- Two sources of light \(0.6 \mathrm{~mm}\) apart and screen is placed at a distance of \(1.2 \mathrm{~m}\) from them. A light of wavelength \(6000 Å\) used. Then the phase difference between the two light waves interfering on the screen at a point at a distance \(3 \mathrm{~mm}\) from central bright band isMHT CET 2023 Medium
- An alternating voltage is applied to a series LCR circuit. If the current leads the voltage by \(45^{\circ}\), then \(\left(\tan 45^{\circ}=1\right)\)MHT CET 2023 Easy
- A monobasic weak acid dissociates \(2 \%\) in its 0.002 M solution.
Calculate the dissociation constant of weak acid.MHT CET 2025 Medium - What is vapour pressure of a solution containing \(1.8 g\) glucose in 16. \(2 \mathrm{~g}\) of water if vapour pressure of water is \(32 \mathrm{~mm} \mathrm{Hg}\) ?MHT CET 2022 Easy