Question 213: Ray Optics

Question

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 :

Accepted Answer

The resolving power (RP) of an optical instrument is inversely proportional to the wavelength (ÃÂ») of light used. So, if we denote the resolving powers corresponding to ÃÂ»Ã¢ÂÂ and ÃÂ»Ã¢ÂÂ as RPÃ¢ÂÂ and RPÃ¢ÂÂ respectively, we can express this relationship as :
RP $ \propto $ ${1 \over \lambda }$
Therefore, the ratio of the resolving powers corresponding to ÃÂ»Ã¢ÂÂ and ÃÂ»Ã¢ÂÂ 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 :
$\frac{RP_1}{RP_2} = \frac{5000 \, 	ext{ÃÂ}}{4000 \, 	ext{ÃÂ}} = \frac{5}{4}$
So, the correct answer is :
Option D : 5 : 4.

Answer

$16:25$

Answer

$9:1$

Answer

$4:5$

Answer

$5:4$

Ray Optics

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 :

Choose the correct answer: