Light of wavelength 500nm traveling with a speed of `2.0xx10^(8)ms^(-1)` in a certain medium enters another medium of refractive index `5//4` times that of the first medium. What are the wavelength and speed in the second medium?

Options

A. Wavelength `(nm)` speed`(ms^(-1))` 400 `1.6xx10^(8)`
B. Wavelength `(nm)` speed`(ms^(-1))` 400 `2.5xx10^(8)`
C. Wavelength `(nm)` speed`(ms^(-1))` 500 `2.5xx10^(8)`
D. Wavelength `(nm)` speed`(ms^(-1))` 625 `1.6xx10^(8)`

Answer

a.

Explanation

The refractive index , `._1n_(2)` (from medium 1 to medium 2) for two given media 1 and 2 is given by
`._1n_(2)=("speed of light in medium 1 "(c_(1)))/("speedof light in medium 2" (c_(2)))`
`=("wave leng th of light in medium 1" (lambda_(1)))/("Wave length of light in medium 2" (lambda_(2)))`
Now, `._1n_(2)=(n_(2))/(n_(1))=(5)/(4)`
`c_(1)=2.0xx10^(-8)ms^(-1)`
`lambda_(1)=500nm`
`:.(5)/(4)=(2.0xx10^(8))/(c_(2))=(500)/(lambda_(2))`
Hence, `lambda_(2)=400nm`
`c_(2)=1.6xx10^(8)ms^(-1)`