An achromatic prism is made by combining two prisms P1 -V- 1-523 - -R- 1-515 and P2 -V-1-666- -r -1-650 - where - represents the refractive index- If the angle of the prism P1 is 10o - then the angle of the prism P2 will be-

The correct option is B 5^o The deviation is given by, δ #160; = ( μ _V μ _R)A The angle of deviation is equal for both the prisms. ∴δ #160; ...

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Standard X

Physics

Minimum Deviation

An achromatic...

Question

An achromatic prism is made by combining two prisms $P_{1} (μ_{V} = 1.523, μ_{R} = 1.515)$ and $P_{2} (μ_{V} = 1.666, μ_{r} = 1.650)$ , where $μ$ represents the refractive index. If the angle of the prism $P_{1}$ is $10^{o}$ , then the angle of the prism $P_{2}$ will be:

5^{o}

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12^{o}

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{10.6}^{o}

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3^{o}

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Solution

The correct option is B $5^{o}$
The deviation is given by,
$δ = (μ_{V} - μ_{R}) A$
The angle of deviation is equal for both the prisms.
$∴ δ = (μ_{V 1} - μ_{R 1}) A_{1} = (μ_{V 2} - μ_{R 2}) A_{2}$
$\Rightarrow (1.523 - 1.515) 10 = (1.666 - 1.650) A_{2}$
$\Rightarrow 0.08 = 0.016 A_{2}$
$A_{2} = \frac{0.08}{0.016} = 5^{\circ}$
Hence the correct answer is option (A).

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An achromatic prism is made by combining two prisms P1 (μV=1.523, μR=1.515) and P2 (μV=1.666, μr=1.650) , where μ represents the refractive index. If the angle of the prism P1 is 10o , then the angle of the prism P2 will be:

The correct option is B 5oThe deviation is given by,δ=(μV−μR)AThe angle of deviation is equal for both the prisms.∴δ=(μV1−μR1)A1=(μV2−μR2)A2⇒(1.523−1.515)10=(1.666−1.650)A2⇒0.08=0.016A2A2=0.080.016=5∘Hence the correct answer is option (A).

An achromatic prism is made by combining two prisms $P_{1} (μ_{V} = 1.523, μ_{R} = 1.515)$ and $P_{2} (μ_{V} = 1.666, μ_{r} = 1.650)$ , where $μ$ represents the refractive index. If the angle of the prism $P_{1}$ is $10^{o}$ , then the angle of the prism $P_{2}$ will be: