' $n$ ' polarizing sheets are arranged such that each makes an angle $45^{\circ}$ with the preceeding sheet An unpolarized light of intensity I is incident into this arrangement The output intensity is found to be $I / 64$ The value of $n$ will be:
- 6
- 5
- 3
- 4
The Correct Option is A
Approach Solution - 1
\(I_1=\frac{I}{2}\)
After passing through the second sheet
\(I_2 = I_1\text{ }cos^{2}(45\degree)= \frac{I}{4}\)
After passing through nth sheet
\(I_n=\frac{I}{2^n}=\frac{I}{64}\)
\(n=6\)
Approach Solution -2
After passing through the first sheet: \[ I_1 = \frac{I}{2} \] After passing through the second sheet: \[ I_2 = I_1 \cos^2(45^\circ) = \frac{I}{4} \] After passing through the \( n \)th sheet: \[ I_n = \frac{I}{2^n} = \frac{I}{64} \] Solving for \( n \), \[ n = 6 \]
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Concepts Used:
Wave Optics
- Wave optics are also known as Physical optics which deal with the study of various phenomena such as polarization, interference, diffraction, and other occurrences where ray approximation of geometric optics cannot be done. Thus, the section of optics that deals with the behavior of light and its wave characteristics is known to be wave optics.
- In wave optics, the approximation is carried out by utilizing ray optics for the estimation of the field on a surface. Further, it includes integrating a ray-estimated field over a mirror, lens, or aperture for the calculation of the transmitted or scattered field.
- Wave optics stands as a witness to a famous standoff between two great scientific communities who devoted their lives to understanding the nature of light. Overall, one supports the particle nature of light; the other supports the wave nature.
- Sir Isaac Newton stood as a pre-eminent figure that supported the voice of particle nature of light, he proposed a corpuscular theory which states that “light consists of extremely light and tiny particles, called corpuscles which travel with very high speeds from the source of light to create a sensation of vision by reflecting on the retina of the eye”.