Trigonometry – JEE First

Oblique beam on a double slit

January 22nd, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 7

In a Young’s double slit experiment, the slit separation $d$ is 0.3 mm and the screen distance $D$ is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point $O$ is equidistant from the slits and distance $P O$ is 11.0 mm. Which of the following statement(s) is/are correct?

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For $\alpha=\frac{0.36}{\pi}$ degree, there will be destructive interference at point $O$ .
For $\alpha=0$ , there will be constructive interference at point $P$ .
For $\alpha=\frac{0.36}{\pi}$ degree, there will be destructive interference at point $P$ .
Fringe spacing

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Total internal reflection from a prism

January 20th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 2, Question 11

A monochromatic light is incident from air on a refracting surface of a prism of angle $75^{\circ}$ and refractive index $n_{0}=\sqrt{3}$ . The other refracting surface of the prism is coated by a thin film of material of refractive index $n$ as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $\theta \leq 60^{\circ}$ . What is the value of $n^{2}$ ?

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Solution

First we trace the given incident ray through the prism to find the angle at which it is incident on the opposite face (see figure below). For …

Delay in a fiber optic cable

January 9th, 2022jeefirst0 Comments

JEE Advanced 2019 Paper 1, Question 18

A planar structure of length $L$ and width $W$ is made of two different optical media of refractive indices $n_{1}=1.5$ and $n_{2}=1.44$ as shown in figure. If $L \gg W$ , a ray entering from end ${\rm AB}$ will emerge from end ${\rm CD}$ only if the total internal reflection condition is met inside the structure. For $L=9.6$ m, if the incident angle $\theta$ is varied, the maximum time taken by a ray to exit the plane $\mathrm{CD}$ is $t \times 10^{-9}$ s. Determine $t$ .

[ Speed of light $c=3 \times 10^{8}$ m/s. ]

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Solution

To ensure that the ray spends the maximum possible time inside the media, we should arrange it so …