A double slit interference experiment performed with a light of wavelength 600nm$600\mathrm{nm}$ forms an interference fringe pattern on a screen with 10th$10^{\mathrm{th}}$ bright fringe having its centre at a distance of 10mm$10\mathrm{mm}$ from the central maximum. Distance of the centre of the same 10th$10^{\mathrm{th}}$ bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660nm$660\mathrm{nm}$ would be ____________________

Related Formula

Core Logic

When unpolarised light of intensity I₀$I_0$ passes through the first polaroid A$\mathrm{A}$, it becomes plane-polarised, and its intensity drops by exactly half.

When this polarised light passes through the second polaroid B$\mathrm{B}$, the transmitted intensity is determined by Malus's Law.

Step 1: Apply Malus's Law

The angle between the principal planes of polaroids A$\mathrm{A}$ and B$\mathrm{B}$ is θ = 45^°$\theta = 45^\circ$.

Pattern Recognition

Unpolarised to Polarised arrow I₀/2$\rightarrow I_0/2$. Polarised to Polarised arrow I ²θ$\rightarrow I \cos^2\theta$. At θ = 45^°$\theta = 45^\circ$, ²θ = 1/2$\cos^2\theta = 1/2$, resulting in a final intensity of I₀/4$I_0/4$.

Chapter Mix

Class 12 Physics: Wave Optics

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Core Logic

In a single slit diffraction pattern, the linear width of any secondary maxima (fringe width of secondary bright bands) is given by W = (λ D)/(a)$W = \frac{\lambda D}{a}$, whereas the central maximum is double this width (2(λ D)/(a)$2\frac{\lambda D}{a}$).

Step 1: Parameter Identification

Given values: Slit width, a = 0.2 × 10⁻³ ~m$a = 0.2 \times 10^{-3} \mathrm{~m}$ Wavelength, λ = 400 × 10⁻⁹ ~m$\lambda = 400 \times 10^{-9} \mathrm{~m}$ Distance to screen (focal length of the lens), D = 100 × 10⁻² ~m = 1 ~m$D = 100 \times 10^{-2} \mathrm{~m} = 1 \mathrm{~m}$

Step 2: Execution

Substitute these into the formula:

Pattern Recognition

Remember to strictly distinguish between central maximum (2λ D/a$2\lambda D/a$) and secondary maxima (λ D/a$\lambda D/a$).

Chapter Mix

Class 12 Physics: Wave Optics

Related Formula

Brewster's Law states that at complete polarization upon reflection, the reflected and refracted rays are perpendicular to each other:

Core Logic

The incident angle is given as iₚ = 60°$i_p = 60^{\circ}$. At this angle, since the reflected ray is completely polarized, the geometry of Brewster's angle applies.

Step 1: Calculate Refraction Angle

Pattern Recognition

The condition "reflected ray is completely polarized" is a direct trigger for Brewster's Law (iₚ + r = 90°$i_p + r = 90^{\circ}$). No refractive index (μ$\mu$) calculation is needed if only the geometric angle is asked.

Chapter Mix

Class 12 Physics: Wave Optics Class 12 Physics: Ray Optics and Optical Instruments

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Core Logic

Let the individual intensities be IA = I₀$I_A = I_0$ and IB = 9I₀$I_B = 9I_0$.

For incoherent waves, the net intensity is simply the algebraic sum:

I₁ = 10I₀$I_1 = 10I_0$

Step 2: Coherent Waves Interference

For coherent waves with a phase difference of φ = 60^°$\phi = 60^\circ$:

Step 3: Finding x

Taking the ratio:

Comparing with the given expression (10)/(x)$\frac{10}{x}$, we get: x = 13$x = 13$

Chapter Mix

Class 12 Physics: Wave Optics