Question

An equilateral prism deviates a ray through $45^{∘}$ for two angles of incidence differing by $20^{∘}$ . The angles of incidence are :

• A. $60^{∘}$ and $40^{∘}$
• B. $50^{∘}$ and $70^{∘}$
• C. $62^{∘}30^{′}$ and $42^{∘}30^{′}$
• D. $60^{∘}30^{′}$ and $40^{∘}30^{′}$

Answer 1

Answer: (C)

$δ={\text{i}}_1+{\text{i}}_2−\text{A}$
$45^{{}^{∘}}={\text{i}}_1+{\text{i}}_2−60^{{}^{∘}}$
${\text{i}}_1+{\text{i}}_2=105^{{}^{∘}}$
${\text{i}}_1−{\text{i}}_2=20^{{}^{∘}}$
or $2{\text{i}}_{\text{i}}=125^{{}^{∘}}$
${\text{i}}_1=62^{{}^{∘}}30^{{}^{′}}\text{, }{\text{i}}_2=42^{{}^{∘}}30^{{}^{′}}$