Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of the angle of incidence?
Answers & Comments
Explanation:
Incident angle must equal or greater than critical angle
critical angle-c
incident angle-i
i≥c
Answer:
The value of the angle of incidence [tex]\mathrm{n} > \sqrt{2}[/tex]
Explanation:
Step 1: A figure made up of two lines that extend from the same spot, whether it be a corner, a projecting part, or a partly enclosed space. a measurement of an angle or the quantity of turning required to align or make parallel two lines or planes. angled.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin term "angulus," which means "corner," is where the word "angle" originates. The shared endpoint of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
Step 2: A pair of rays (half-lines) with a shared endpoint are combined to form an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its limbs.
[tex]\text { If } \theta_{\mathrm{i}}=90^{\circ} \text { then, Snell's law, }[/tex]
[tex]\begin{aligned}& 1 \sin \theta_{\mathrm{i}}=\mathrm{n} \sin \theta_{\mathrm{r}} \\& \sin \theta_{\mathrm{r}}=\frac{1}{\mathrm{n}} \ldots \ldots \ldots \ldots . . \text { (i) }\end{aligned}[/tex]
For all other cases, if this ray just brushes the surface on the lateral edge, I
There will then be complete internal reflection at the side surface I 90 o).
[tex]$\mathrm{n} \sin \left(90-\theta_{\mathrm{r}}\right)=1 \sin 90^{\circ}$$\mathrm{n} \cos \theta_{\mathrm{r}}=1$From equation (i)$$\begin{aligned}& \mathrm{n} \times \frac{\sqrt{\mathrm{n}^2-1}}{\mathrm{n}}=1 \\& \mathrm{n}^2=2 \\& \mathrm{n}=\sqrt{2}\end{aligned}$$[/tex]
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