282677
Glass prism having a refractive index \(\mu\), placed in a air, for that angle of minimum deviation of prism is same as angle of prism. Then what is value of angle of prism?
1 \(2 \cos ^{-1}(\mu / 2)\)
2 \(2 \cos ^{-1}(\mu)\)
3 \(\cos ^{-1}(\mu / 2)\)
4 \(\cos ^{-1}(\mu)\)
Explanation:
A: Given, \(\delta_{\mathrm{m}}=\mathrm{A}\), Where, \(\mathrm{A}=\) angle of prism We know that,
\(\begin{aligned}
\mu=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin A / 2} \\
\mu=\frac{\sin A}{\sin (A / 2)} \\
\mu=\frac{2 \sin (A / 2) \cos (A / 2)}{\sin (A / 2)} \\
\mu=2 \cos \left(\frac{A}{2}\right) \\
\cos \frac{A}{2}=\frac{\mu}{2}
\end{aligned}\)
So, angle of prism-
\(A=2 \cdot \cos ^{-1}(\mu / 2)\)
GUJCET-PCE- 2021
Ray Optics
282678
A prism is made of a glass having refractive index \(\sqrt{2}\). If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is
282679
A thin glass prism of angle \(9^{\circ}\) with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle (A) of the second prism.
1 \(9^{\circ}\)
2 \(12^{\circ}\)
3 \(6^{\circ}\)
4 \(4^{\circ}\)
Explanation:
C: Given, \(\mu_1=1.4, \mu_2=1.6\)
\(A_1=9^{\circ}, A_2=\text { ? }\)
For no deviation through a prism combination
\(\begin{aligned}
\mathrm{A}_1\left(\mu_1-1\right)=\mathrm{A}_2\left(\mu_2-1\right) \\
\mathrm{A}_2=\mathrm{A}_1 \frac{\left(\mu_1-1\right)}{\left(\mu_2-1\right)} \\
\mathrm{A}_2=9^{\circ} \frac{(1.4-1)}{(1.6-1)}=9^{\circ} \times \frac{0.4}{0.6} \\
\mathrm{~A}_2=6^{\circ}
\end{aligned}\)
TS- EAMCET-14.09.2020
Ray Optics
282680
When a glass prism of refracting angle \(60^{\circ}\) is immersed in a liquid its angle of minimum deviation is \(30^{\circ}\). The critical angle of glass with respect to the liquid medium is
282677
Glass prism having a refractive index \(\mu\), placed in a air, for that angle of minimum deviation of prism is same as angle of prism. Then what is value of angle of prism?
1 \(2 \cos ^{-1}(\mu / 2)\)
2 \(2 \cos ^{-1}(\mu)\)
3 \(\cos ^{-1}(\mu / 2)\)
4 \(\cos ^{-1}(\mu)\)
Explanation:
A: Given, \(\delta_{\mathrm{m}}=\mathrm{A}\), Where, \(\mathrm{A}=\) angle of prism We know that,
\(\begin{aligned}
\mu=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin A / 2} \\
\mu=\frac{\sin A}{\sin (A / 2)} \\
\mu=\frac{2 \sin (A / 2) \cos (A / 2)}{\sin (A / 2)} \\
\mu=2 \cos \left(\frac{A}{2}\right) \\
\cos \frac{A}{2}=\frac{\mu}{2}
\end{aligned}\)
So, angle of prism-
\(A=2 \cdot \cos ^{-1}(\mu / 2)\)
GUJCET-PCE- 2021
Ray Optics
282678
A prism is made of a glass having refractive index \(\sqrt{2}\). If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is
282679
A thin glass prism of angle \(9^{\circ}\) with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle (A) of the second prism.
1 \(9^{\circ}\)
2 \(12^{\circ}\)
3 \(6^{\circ}\)
4 \(4^{\circ}\)
Explanation:
C: Given, \(\mu_1=1.4, \mu_2=1.6\)
\(A_1=9^{\circ}, A_2=\text { ? }\)
For no deviation through a prism combination
\(\begin{aligned}
\mathrm{A}_1\left(\mu_1-1\right)=\mathrm{A}_2\left(\mu_2-1\right) \\
\mathrm{A}_2=\mathrm{A}_1 \frac{\left(\mu_1-1\right)}{\left(\mu_2-1\right)} \\
\mathrm{A}_2=9^{\circ} \frac{(1.4-1)}{(1.6-1)}=9^{\circ} \times \frac{0.4}{0.6} \\
\mathrm{~A}_2=6^{\circ}
\end{aligned}\)
TS- EAMCET-14.09.2020
Ray Optics
282680
When a glass prism of refracting angle \(60^{\circ}\) is immersed in a liquid its angle of minimum deviation is \(30^{\circ}\). The critical angle of glass with respect to the liquid medium is
282677
Glass prism having a refractive index \(\mu\), placed in a air, for that angle of minimum deviation of prism is same as angle of prism. Then what is value of angle of prism?
1 \(2 \cos ^{-1}(\mu / 2)\)
2 \(2 \cos ^{-1}(\mu)\)
3 \(\cos ^{-1}(\mu / 2)\)
4 \(\cos ^{-1}(\mu)\)
Explanation:
A: Given, \(\delta_{\mathrm{m}}=\mathrm{A}\), Where, \(\mathrm{A}=\) angle of prism We know that,
\(\begin{aligned}
\mu=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin A / 2} \\
\mu=\frac{\sin A}{\sin (A / 2)} \\
\mu=\frac{2 \sin (A / 2) \cos (A / 2)}{\sin (A / 2)} \\
\mu=2 \cos \left(\frac{A}{2}\right) \\
\cos \frac{A}{2}=\frac{\mu}{2}
\end{aligned}\)
So, angle of prism-
\(A=2 \cdot \cos ^{-1}(\mu / 2)\)
GUJCET-PCE- 2021
Ray Optics
282678
A prism is made of a glass having refractive index \(\sqrt{2}\). If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is
282679
A thin glass prism of angle \(9^{\circ}\) with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle (A) of the second prism.
1 \(9^{\circ}\)
2 \(12^{\circ}\)
3 \(6^{\circ}\)
4 \(4^{\circ}\)
Explanation:
C: Given, \(\mu_1=1.4, \mu_2=1.6\)
\(A_1=9^{\circ}, A_2=\text { ? }\)
For no deviation through a prism combination
\(\begin{aligned}
\mathrm{A}_1\left(\mu_1-1\right)=\mathrm{A}_2\left(\mu_2-1\right) \\
\mathrm{A}_2=\mathrm{A}_1 \frac{\left(\mu_1-1\right)}{\left(\mu_2-1\right)} \\
\mathrm{A}_2=9^{\circ} \frac{(1.4-1)}{(1.6-1)}=9^{\circ} \times \frac{0.4}{0.6} \\
\mathrm{~A}_2=6^{\circ}
\end{aligned}\)
TS- EAMCET-14.09.2020
Ray Optics
282680
When a glass prism of refracting angle \(60^{\circ}\) is immersed in a liquid its angle of minimum deviation is \(30^{\circ}\). The critical angle of glass with respect to the liquid medium is
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Ray Optics
282677
Glass prism having a refractive index \(\mu\), placed in a air, for that angle of minimum deviation of prism is same as angle of prism. Then what is value of angle of prism?
1 \(2 \cos ^{-1}(\mu / 2)\)
2 \(2 \cos ^{-1}(\mu)\)
3 \(\cos ^{-1}(\mu / 2)\)
4 \(\cos ^{-1}(\mu)\)
Explanation:
A: Given, \(\delta_{\mathrm{m}}=\mathrm{A}\), Where, \(\mathrm{A}=\) angle of prism We know that,
\(\begin{aligned}
\mu=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin A / 2} \\
\mu=\frac{\sin A}{\sin (A / 2)} \\
\mu=\frac{2 \sin (A / 2) \cos (A / 2)}{\sin (A / 2)} \\
\mu=2 \cos \left(\frac{A}{2}\right) \\
\cos \frac{A}{2}=\frac{\mu}{2}
\end{aligned}\)
So, angle of prism-
\(A=2 \cdot \cos ^{-1}(\mu / 2)\)
GUJCET-PCE- 2021
Ray Optics
282678
A prism is made of a glass having refractive index \(\sqrt{2}\). If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is
282679
A thin glass prism of angle \(9^{\circ}\) with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle (A) of the second prism.
1 \(9^{\circ}\)
2 \(12^{\circ}\)
3 \(6^{\circ}\)
4 \(4^{\circ}\)
Explanation:
C: Given, \(\mu_1=1.4, \mu_2=1.6\)
\(A_1=9^{\circ}, A_2=\text { ? }\)
For no deviation through a prism combination
\(\begin{aligned}
\mathrm{A}_1\left(\mu_1-1\right)=\mathrm{A}_2\left(\mu_2-1\right) \\
\mathrm{A}_2=\mathrm{A}_1 \frac{\left(\mu_1-1\right)}{\left(\mu_2-1\right)} \\
\mathrm{A}_2=9^{\circ} \frac{(1.4-1)}{(1.6-1)}=9^{\circ} \times \frac{0.4}{0.6} \\
\mathrm{~A}_2=6^{\circ}
\end{aligned}\)
TS- EAMCET-14.09.2020
Ray Optics
282680
When a glass prism of refracting angle \(60^{\circ}\) is immersed in a liquid its angle of minimum deviation is \(30^{\circ}\). The critical angle of glass with respect to the liquid medium is
