For which of the following colours of monochromatic light, the fringe width in the interference fringe pattern observed in a Fresnel's biprism experiment will be maximum?
Red
Fringe Width in Fresnel's Biprism
The question asks about the colour of monochromatic light that produces the maximum fringe width in an interference fringe pattern observed in a Fresnel's biprism experiment. To understand this, we need to recall the formula for fringe width in an interference setup.
Understanding Fringe Width Formula
In an interference experiment, like the one involving Fresnel's biprism or Young's double-slit experiment, the fringe width ($\beta$) is given by the formula:
$$\beta = \frac{\lambda D}{d}$$
Where:
- \(\beta\) represents the fringe width, which is the distance between two consecutive bright fringes or two consecutive dark fringes.
- \(\lambda\) represents the wavelength of the monochromatic light used.
- \(D\) represents the distance from the sources (or virtual sources in the case of a biprism) to the screen where the interference pattern is observed.
- \(d\) represents the distance between the two coherent virtual sources produced by the Fresnel's biprism.
Wavelength and Fringe Width Relationship
From the formula, it is clear that the fringe width (\(\beta\)) is directly proportional to the wavelength (\(\lambda\)) of the light used, assuming \(D\) and \(d\) remain constant for a given experimental setup.
This means:
- If the wavelength of light increases, the fringe width will also increase.
- If the wavelength of light decreases, the fringe width will also decrease.
Monochromatic Light and Wavelength
Monochromatic light refers to light of a single wavelength. Visible light consists of a spectrum of colours, each corresponding to a different range of wavelengths. The approximate wavelengths for the colours mentioned in the options are:
| Colour | Approximate Wavelength Range (in nanometers, nm) |
|---|---|
| Blue | 450 - 495 nm |
| Green | 495 - 570 nm |
| Yellow | 570 - 590 nm |
| Red | 620 - 750 nm |
From this table, it is evident that red light has the longest wavelength among the given options (Green, Red, Yellow, Blue). Blue light has the shortest wavelength among these options.
Maximizing Fringe Width
Since the fringe width is directly proportional to the wavelength, to achieve the maximum fringe width, we must use the monochromatic light with the longest wavelength. Based on the visible spectrum, red light has the longest wavelength.
Therefore, for red monochromatic light, the fringe width observed in the interference fringe pattern in a Fresnel's biprism experiment will be maximum.
Important Questions from Interference
- A single slit of width $a$ is illuminated by a monochromatic light of wavelength $\lambda_1 = 6000 \text{ Å}$. The angular width of the central maximum observed in the Fraunhofer diffraction pattern is $\theta_1$. When the slit width is increased by $20\%$ and the light source is replaced with another monochromatic light of wavelength $\lambda_2$, the angular width of the central maximum becomes $\frac{3}{5}$ of its initial value, $\theta_1$. Determine the wavelength $\lambda_2$.
A system of three polarizers $P_1$, $P_2$, $P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$.
The pass axis of $P_2$ is inclined at $15^\circ$ to the pass axis of $P_1$.
When a beam of unpolarized light of intensity $I_0$ is incident on $P_1$, the intensity of light transmitted by the three polarizers is $I$. The ratio $(I_0/I)$ equals (nearly):The interference pattern is obtained with two coherent light sources. If the ratio of their amplitudes is $n$, then in the interference pattern, the ratio $\frac{{{I_{max}} - {I_{min}}}}{{{I_{max}} + {I_{min}}}}$ will be
- Two identical coherent waves are superimposed at a point. If the maximum possible resultant intensity from their interference is $I_{max}$, and the resultant intensity at this point is $I_{max}/4$, then find the phase difference between the two waves at this point.
Which of the following sources gives best monochromatic light?
