Physics · Wave Optics · NEET
Fringe width beta = lambda*D/d. Here lambda is the wavelength of light, D is the distance from the slits to the screen, and d is the gap between the two slits. beta is the distance between two neighbouring bright (or dark) fringes. Bright and dark fringes have the same width. The angular fringe width is theta = beta/D = lambda/d, which does not depend on D.
In single-slit diffraction, a*sin(theta) = n*lambda (with n = 1, 2, 3...) gives the DARK bands (minima). This is the opposite of YDSE, where n*lambda gives BRIGHT fringes. The secondary maxima of a single slit are roughly at a*sin(theta) = (2n+1)*lambda/2. Mixing up the single-slit and double-slit conditions is the most common NEET slip.
Phase difference phi = (2*pi/lambda) * (path difference). So a path difference of one full lambda equals a phase difference of 2*pi (360 degrees), and lambda/2 equals pi (180 degrees). Bright fringe: path difference = n*lambda. Dark fringe: path difference = (2n-1)*lambda/2.
For two coherent waves, resultant intensity I = I_1 + I_2 + 2*sqrt(I_1*I_2)*cos(phi). If both waves have equal intensity I_0, this becomes I = 4*I_0*cos^2(phi/2), and I_max = 4*I_0, I_min = 0. The ratio I_max/I_min = ((sqrt(I_1)+sqrt(I_2))/(sqrt(I_1)-sqrt(I_2)))^2, or in amplitude form ((a_1+a_2)/(a_1-a_2))^2.
Malus's law: when polarised light of intensity I_0 passes through a polaroid whose axis is at angle theta, transmitted intensity I = I_0*cos^2(theta). For unpolarised light hitting the first polaroid, output is I_0/2 (average of cos^2 is 1/2). Brewster's law: at the polarising angle, tan(i_B) = mu, and the reflected and refracted rays are perpendicular (i_B + r = 90 degrees). The reflected light is fully polarised.
Limit of resolution (smallest angle you can just separate): d_theta = 1.22*lambda/D for a telescope, where D is the objective diameter. Resolving power = 1/d_theta = D/(1.22*lambda). For a microscope, resolving power = 2*mu*sin(beta)/(1.22*lambda) (the numerator 2*mu*sin(beta) is the numerical aperture term). Both improve when wavelength lambda is smaller.
Fresnel distance Z_F = a^2/lambda, where a is the aperture (slit) size. For distances less than Z_F the beam is roughly a straight ray (ray optics works); beyond Z_F diffraction spreading becomes important. This marks where ray optics breaks down.
A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5 x 10^-5 cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is
Light of wavelength 600 nm is coming from a star. The limit of resolution of a telescope whose objective has a diameter of 2 m is
In Young's double slit experiment, using monochromatic light of wavelength lambda, the intensity of light at a point where the path difference is lambda is K units. The intensity at a point where the path difference is lambda/3 will be
Try the real previous-year questions from this chapter — each with the answer and a full solution.
YDSE formulas dominate: fringe width beta = lambda*D/d and intensity I = I_max*cos^2(phi/2). Single-slit diffraction a*sin(theta) = n*lambda, resolving power 1.22*lambda/D, Malus law, and Brewster's law each appear regularly too. Learn these six and you cover most questions.
Yes. Inside a medium of refractive index mu, wavelength becomes lambda/mu, so fringe width becomes beta/mu (fringes get closer). Frequency and colour stay the same; only wavelength and speed change.
Fringe width beta = lambda*D/d is a length on the screen and depends on D. Angular fringe width theta = lambda/d is an angle and does NOT depend on D. Moving the screen changes beta but not the angular width.
For single-slit diffraction it gives the DARK minima. For double-slit (YDSE) the same form d*sin(theta) = n*lambda gives BRIGHT maxima. Always check single vs double slit first.
The 1.22 comes from the diffraction pattern of a circular aperture (the first dark ring of the Airy pattern). It is a fixed constant for round openings like telescope and microscope apertures.
