Question

In a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0 ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light 21.2 ns to travel from the laser to the photocell. What is the wavelength of the light in the glass?

Answer 1

Answer:196 nm

Explanation:

Given

wavelength $\lambda =490 nm$

time required by laser to travel in air $t_1=17 ns$

slab thickness $t=0840 m$

time requires by laser to travel $t_2=21.2 ns$

so it takes $21.2-17=4.2 ns$ more in glass slab

suppose n is the refractive index of glass

$\frac{0.84}{\frac{c}{n}}-\frac{0.84}{c}=4.2$

$0.84(n-1)=4.2\times 3\times 10^{-9}\times 10^{8}$

n-1=1.5

n=2.5

Wavelength of light in Glass$=\frac{\lambda _{air}}{n}$

$=\frac{490}{2.5}=196 nm$