Dispersion without deviation is produced by two thin (small angled) prisms which are combined together. One prism has angle 5° and refractive index 1.56 . If the other prism has refractive index 1.7 , what is its angle ?

Question

Dispersion without deviation is produced by two thin (small angled) prisms which are combined together. One prism has angle 5° and refractive index 1.56 . If the other prism has refractive index 1.7 , what is its angle ? (A)  3°  (B)  4°  (C)  5°  (D)  6°

Tardigrade Admin · Accepted Answer

Dispersion without deviation by combining two prisms of angles

A_{1}

and

A_{2}

with refractive indices

n_{1}

and

n_{2}

is given by

(n_{1} - 1) A_{1} = (n_{2} - 1) A_{2} \dots (i)

Here

n_{1} = 1.56, A_{1} = 5^{\circ}, n_{2} = 1.7

From equation (i),

\Rightarrow (1.56 - 1) \times 5

= (1.7 - 1) \times A_{2}; A_{2} = 4^{\circ}

Q. Dispersion without deviation is produced by two thin (small angled) prisms which are combined together. One prism has angle $5^{\circ}$ and refractive index $1.56$ . If the other prism has refractive index $1.7$ , what is its angle ?

$3^{\circ}$

$4^{\circ}$

$5^{\circ}$

$6^{\circ}$

Q. Dispersion without deviation is produced by two thin (small angled) prisms which are combined together. One prism has angle 5∘ and refractive index 1.56 . If the other prism has refractive index 1.7 , what is its angle ?

3∘

4∘

5∘

6∘

Dispersion without deviation by combining two prisms of angles A1​ and A2​ with refractive indices n1​ and n2​ is given by (n1​−1)A1​=(n2​−1)A2​…(i) Here n1​=1.56,A1​=5∘,n2​=1.7 From equation (i), ⇒(1.56−1)×5 =(1.7−1)×A2​;A2​=4∘

Q. Dispersion without deviation is produced by two thin (small angled) prisms which are combined together. One prism has angle $5^{\circ}$ and refractive index $1.56$ . If the other prism has refractive index $1.7$ , what is its angle ?

$3^{\circ}$

$4^{\circ}$

$5^{\circ}$

$6^{\circ}$