Question:
A glass plate of refractive index $1.5$ is coated with a thin layer of thickness t and refractive index $1.8$. Light of wavelength $648 \,nm$ travelling in air is incident normally on the layer. It is partly reflected at upper and lower surfaces of the layer and the two reflected rays interfere. The least value of $t$ for which the rays interfere constructively is
A glass plate of refractive index $1.5$ is coated with a thin layer of thickness t and refractive index $1.8$. Light of wavelength $648 \,nm$ travelling in air is incident normally on the layer. It is partly reflected at upper and lower surfaces of the layer and the two reflected rays interfere. The least value of $t$ for which the rays interfere constructively is
Updated On: Jun 14, 2022
- 30 nm
- 60 nm
- 90 nm
- 120nm
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The Correct Option is C
Solution and Explanation
Given $\mu=$ refractive index of glass $=1.5 $
$t =$ thickness of coating,
$\mu=$ refractive index of coating $=1.8\, \lambda$
$=648 \times 10^{-9} m$
For constructive interference $2 \,\mu t=(2 n+1) \frac{\lambda}{2}$
$2 \times 1.8 \times t=\frac{648 \times 10^{-9}}{2}$
($t$ to be minimum $n =0$ )
$t=\frac{648}{2 \times 2 \times 1.8} \times 10^{-9} m$
$t=\frac{648}{7.2} \times 10^{-9} m=90 \,m$
$t =$ thickness of coating,
$\mu=$ refractive index of coating $=1.8\, \lambda$
$=648 \times 10^{-9} m$
For constructive interference $2 \,\mu t=(2 n+1) \frac{\lambda}{2}$
$2 \times 1.8 \times t=\frac{648 \times 10^{-9}}{2}$
($t$ to be minimum $n =0$ )
$t=\frac{648}{2 \times 2 \times 1.8} \times 10^{-9} m$
$t=\frac{648}{7.2} \times 10^{-9} m=90 \,m$
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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”.