YDSE Intensity Formula
In Young's double-slit experiment (YDSE), when two coherent waves of equal intensity $I_o$ from each slit interfere, the resultant intensity $I$ at any point on the screen depends on the phase difference ($\delta$) between the waves arriving at that point.
The formula for the resultant intensity is:
$I = I_o + I_o + 2\sqrt{I_o \cdot I_o} \cos(\delta)$
This formula simplifies to:
$I = 2I_o (1 + \cos(\delta))$
Intensity Calculation for $2I_o$
To find the intensity value of $2I_o$, we set $I = 2I_o$ in the intensity formula:
$2I_o = 2I_o (1 + \cos(\delta))$
Dividing both sides by $2I_o$ yields:
$1 = 1 + \cos(\delta)$
This equation implies that:
$\cos(\delta) = 0$
The condition $\cos(\delta) = 0$ occurs when the phase difference $\delta$ is $\frac{\pi}{2}$ or $\frac{3\pi}{2}$ (or any odd multiple thereof). This corresponds to specific points on the screen where the path difference is $\Delta r = \frac{\lambda}{4}$ or $\Delta r = \frac{3\lambda}{4}$. At these points, the intensity is $2I_o$. While the phrasing "in front of one of the slits" can be ambiguous, the intensity value $2I_o$ is achieved under the condition $\cos(\delta) = 0$.
Therefore, the intensity on the screen is $2I_o$.
Similar Questions
- Distance between an object and three times magnified real image is $40 \text{ cm}$. The focal length of the mirror used is _______ cm.
- A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will
- Five persons $\text{P}_1, \text{P}_2, \text{P}_3, \text{P}_4 \text{ and } \text{P}_5$ recorded object distance ($u$) and image distance ($v$) using same convex lens having power $+5\text{D}$ as $(25, 96), (30, 62), (35, 37), (45, 35)$ and $(50, 32)$ respectively. Identify correct statement
- In a microscope the objective is having focal length $f_o = 2 \text{ cm}$ and eye-piece is having focal length $f_e = 4 \text{ cm}$. The tube length is $32 \text{ cm}$. The magnification produced by this microscope for normal adjustment is ____________.
- A collimated beam of light of diameter $2 \text{ mm}$ is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter $14 \text{ mm}$ using a system of two convex lenses. If first lens has focal length $40 \text{ mm}$, then the focal length of second lens is ____________ $\text{mm}$.
As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.
If refractive index of the material of prism is $\sqrt{2}$, the angle $\theta$ of prism is.- Given below are two statements :
Statement I : In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength
In the light of the above statements, choose the correct answer from the options given below : - In a Young's double slit experiment set up, the two slits are kept $0.4\text{ mm}$ apart and screen is placed at $1\text{ m}$ from slits. If a thin transparent sheet of thickness $20 \, \mu\text{m}$ is introduced in front of one of the slits then center bright fringe shifts by $20\text{ mm}$ on the screen. The refractive index of transparent sheet is given by $\frac{\alpha}{10}$, where $\alpha$ is __________.
- For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index $n$ of the prism satisfies.
- Consider light travelling from a medium $A$ to medium $B$ separated by a plane interface. If the light undergoes total internal reflection during its travel from medium $A$ to $B$ and the speed of light in media $A$ and $B$ are $2.4 \times 10^8\text{ m/s}$ and $2.7 \times 10^8\text{ m/s}$, respectively, then the value of critical angle is :
Important Questions from Optics
- Distance between an object and three times magnified real image is $40 \text{ cm}$. The focal length of the mirror used is _______ cm.
- A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will
- Five persons $\text{P}_1, \text{P}_2, \text{P}_3, \text{P}_4 \text{ and } \text{P}_5$ recorded object distance ($u$) and image distance ($v$) using same convex lens having power $+5\text{D}$ as $(25, 96), (30, 62), (35, 37), (45, 35)$ and $(50, 32)$ respectively. Identify correct statement
- In a microscope the objective is having focal length $f_o = 2 \text{ cm}$ and eye-piece is having focal length $f_e = 4 \text{ cm}$. The tube length is $32 \text{ cm}$. The magnification produced by this microscope for normal adjustment is ____________.
- A collimated beam of light of diameter $2 \text{ mm}$ is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter $14 \text{ mm}$ using a system of two convex lenses. If first lens has focal length $40 \text{ mm}$, then the focal length of second lens is ____________ $\text{mm}$.
