Polarization — Brewster's law, Malus' law
Wave Optics
8
JEE Qs
8%
Hard
60
min
Always clearly identify the polarization state (unpolarized, partially polarized, plane-polarized) and intensity of light at each stage of a problem before applying Brewster's or Malus' law.
🧮 Key Formulas
✅ Key Points for JEE
- 1Unpolarized light has electric field vibrations in all possible planes perpendicular to the direction of propagation. Plane-polarized light has vibrations restricted to a single plane.
- 2Brewster's Law states that when unpolarized light is incident at a specific angle (Brewster's angle, i_p) on an interface, the reflected light is completely plane-polarized (electric field oscillations perpendicular to the plane of incidence) and the reflected and refracted rays are perpendicular to each other.
- 3Malus' Law applies when plane-polarized light of intensity I_0 passes through an analyzer. The transmitted intensity I depends on the angle (theta) between the direction of polarization of the incident light and the transmission axis of the analyzer as I = I_0 cos^2(theta).
- 4A single ideal polaroid reduces the intensity of incident unpolarized light by half (I = I_0_unpolarized / 2) and polarizes it.
- 5The refractive index 'n' in Brewster's law (tan(i_p) = n) refers to the refractive index of the medium from which reflection occurs, relative to the incident medium (often air, so n_2/n_1 where n_1=1).
⚠️ Common Mistakes
- ✕Confusing the initial intensity I_0 in Malus' law: it must be the intensity of *plane-polarized* light incident on the analyzer, not unpolarized light.
- ✕Incorrectly identifying the angle 'theta' in Malus' law: it is the angle between the plane of vibration of the *incident polarized light* and the transmission axis of the analyzer.
- ✕Assuming the refracted light at Brewster's angle is completely polarized; it is only partially polarized, while the reflected light is completely plane-polarized.
- ✕Forgetting to halve the intensity of unpolarized light when it first passes through a polaroid before applying Malus' law if subsequent polaroids are involved.
📝 Practice Questions
See allQ34.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R): The fringe width is directly proportional to the wavelength of light. In the light of the above statements, choose the correct answer from the options given below : (1) Both (A) and (R) are true but (R) is NOT the (2) (A) is true but (R) is false correct explanation of (A) (3) Both (A) and (R) are true and (R) is the correct (4) (A) is false but (R) is true explanation of (A)
Q41.The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is (1) 5 (2) 4 (3) 6 (4) 8
Q43.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true but (R) is not the (2) Both (A) and (R) are true and (R) is the correct correct explanation of (A) explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true
Q31.A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.] (1) 137.5 nm (2) 275 nm (3) 94.8 nm (4) 68.7 nm
Q37. Using the given P −V diagram, the work done by an ideal gas along the path ABCD is : (1) 3P0 V0 (2) −4P0 V0 (3) −3P0 V0 (4) 4P0 V0
Q29.Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be : (1) 0.23 mm (2) 0.33 mm (3) 0.63 mm (4) 0.46 mm
NCERT Chapters
- Class 12 Physics Ch 10: Wave Optics