Young's Double-Slit: Fringe Width Calculation
The fringe width ($\beta$) in Young's double-slit experiment is determined by the wavelength of light ($\lambda$), the distance between the slits and the screen ($D$), and the separation between the slits ($d$). The formula is:
$ \beta = \frac{\lambda D}{d} $
Equal Fringe Width Condition
The problem states that two separate experimental set-ups produce fringes of equal width. Let the parameters for the two set-ups be subscripted with 1 and 2.
Therefore, we have:
$ \beta_1 = \beta_2 $
Substituting the formula for fringe width:
$ \frac{\lambda_1 D_1}{d_1} = \frac{\lambda_2 D_2}{d_2} $
Calculating the Distance Ratio
We need to find the ratio of the distances between the slits and the screens, which is $D_1/D_2$. Rearranging the equation from the previous step:
$ \frac{D_1}{D_2} = \frac{\lambda_2}{\lambda_1} \times \frac{d_1}{d_2} $
Applying Given Ratios
The problem provides the following ratios:
- Ratio of slit separations: $d_1 : d_2 = 2 : 1 \implies \frac{d_1}{d_2} = \frac{2}{1}$
- Ratio of wavelengths: $\lambda_1 : \lambda_2 = 1 : 2 \implies \frac{\lambda_1}{\lambda_2} = \frac{1}{2}$. This implies $\frac{\lambda_2}{\lambda_1} = \frac{2}{1}$.
Substitute these values into the rearranged equation:
$ \frac{D_1}{D_2} = \left(\frac{2}{1}\right) \times \left(\frac{2}{1}\right) $
$ \frac{D_1}{D_2} = \frac{4}{1} $
The corresponding ratio of the distances ($D_1/D_2$) is 4.
Similar Questions
- 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 the Young's double slit experiment the intensity produced by each one of the individual slits is $I_o$. The distance between two slits is $2 \text{ mm}$. The distance of screen from slits is $10 \text{ m}$. The wavelength of light is $6000 \text{ \AA}$. The intensity of light on the screen in front of one of the slits is _______.
- 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
- 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 the Young's double slit experiment the intensity produced by each one of the individual slits is $I_o$. The distance between two slits is $2 \text{ mm}$. The distance of screen from slits is $10 \text{ m}$. The wavelength of light is $6000 \text{ \AA}$. The intensity of light on the screen in front of one of the slits is _______.
- 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 ____________ $\text{mm}$.
