Question

Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are m_r, m_y and m_v respectively and those for the flint glass are , and $\mu _ { \mathrm { v } } ^ { \prime }$ respectively. Find the ratio $\frac { \mathrm { A } ^ { \prime } } { \mathrm { A } }$ for which, there is no net angular dispersion.

• A. $\frac { \mu _ { \mathrm { y } } - 1 } { \mu _ { \mathrm { y } } ^ { \prime } - 1 }$
• B. $\frac { 2 \left( \mu _ { \mathrm { v } } - \mu _ { \mathrm { r } } \right) } { \left( \mu _ { \mathrm { v } } ^ { \prime } - \mu _ { \mathrm { r } } ^ { \prime } \right) }$
• C. $\frac { \mu _ { \mathrm { v } } - \mu _ { \mathrm { r } } } { \mu _ { \mathrm { v } } ^ { \prime } - \mu _ { \mathrm { r } } ^ { \prime } }$
• D.

Answer 1

Answer: (B)

$\frac { 2 \left( \mu _ { \mathrm { v } } - \mu _ { \mathrm { r } } \right) } { \left( \mu _ { \mathrm { v } } ^ { \prime } - \mu _ { \mathrm { r } } ^ { \prime } \right) }$

Answer 2

For no net angular dispersion

q_Net = q₁ – q₂ + q₃ = 0

q₂ = q₁ + q₃

(m'_v – m'_r) A' = (m_v – m_r) A + (m_v – m_r)A