Aflat sheet of ice has a thickness of 2.12 cm. it is on top of a flat sheet of fused quartz that has a thickness of 1.24 cm. light strikes the ice perpendicularly and travels through it and then through the fused quartz. in the time it takes the light to travel through the two sheets, how far (in cm) would it have traveled in a vacuum?

4.674 cm

Explanation:

refractive index of ice μ₁ = 1.309

refractive index of quartz μ₂ = 1.544

Velocity of light in ice v₁ = c/μ₁

= 3 x 10⁸ / 1.309

= 2.292 x 10⁸

Velocity of light in quartz v₂ = c/μ₂

= 3 x 10⁸ / 1.544

= 1.943 x 10⁸

Total time taken by light to pass through ice

= 2.12 x 10⁻²/ (2.292 x 10⁸ )

= .92 x 10⁻¹⁰ s

Total time taken by light to pass through quartz

= 1.24 x 10⁻²/ (1.943 x 10⁸ )

= .638 x 10⁻¹⁰ s

Total time taken

=  .92 x 10⁻¹⁰ + .638 x 10⁻¹⁰

= 1.558 x 10⁻¹⁰ s

velocity of light in vacuum

= 3 x 10⁸ m /s

distance travelled in 1.558 x 10⁻¹⁰ s

= 3 x 10⁸ x 1.558 x 10⁻¹⁰

= 4.674 x 10⁻² m

4.674 cm

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y