JEE MAIN - Physics (2002 - No. 17)
Wavelength of light used in an optical instrument are $${\lambda _1} = 4000\mathop A\limits^ \circ $$ and $${\lambda _2} = 5000\mathop A\limits^ \circ ,$$ then ratio of their respective resolving powers (corresponding to $${\lambda _1}$$ and $${\lambda _2}$$ ) is :
$$16:25$$
$$9:1$$
$$4:5$$
$$5:4$$
Explanation
The resolving power (RP) of an optical instrument is inversely proportional to the wavelength (λ) of light used. So, if we denote the resolving powers corresponding to λ₁ and λ₂ as RP₁ and RP₂ respectively, we can express this relationship as :
RP $$ \propto $$ $${1 \over \lambda }$$
Therefore, the ratio of the resolving powers corresponding to λ₁ and λ₂ is given by the inverse of the ratio of the wavelengths. In LaTeX notation, this relationship can be written as :
$\frac{RP_1}{RP_2} = \frac{\lambda_2}{\lambda_1}$
Substituting the given wavelengths into this equation, we get :
$\frac{RP_1}{RP_2} = \frac{5000 \, \text{Å}}{4000 \, \text{Å}} = \frac{5}{4}$
So, the correct answer is :
Option D : 5 : 4.
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