A ray of lightis incident on an air-glass boundary at an angle ɵ. if the ange
between the partialy reflected ray and the refracted rays 90,calculate ɵ,
0
given that the refractive index of glass is 1.50.
When a ray of light is incident on an air-glass boundary, it undergoes refraction. The angle of refraction (r) can be calculated using Snell's Law:
n1 x sin(i) = n2 x sin(r)
Where:
n1 = refractive index of air = 1.00
n2 = refractive index of glass = 1.50
i = angle of incidence = θ
1.00 x sin(θ) = 1.50 x sin(r)
sin(θ) = 1.50 x sin(r)
Given that the angle between the partially reflected ray and the refracted ray is 90 degrees, we can say that:
90 = θ + r
90 = θ + arcsin(1.50 x sin(r))
Substitute sin(r) from the equation above into the equation for 90 degrees:
90 = θ + arcsin(1.50 x 1.50 x sin(θ))
90 = θ + arcsin(2.25 x sin(θ))
Now, we can solve for θ using a numerical method or a graphing calculator.
By solving this equation above, we can find the value of θ in degrees.