A glass plate whose index of refraction is 1.66 is immersed in a liquid. The surface of the glass is inclined at an angle of 44º with the vertical. A horizontal ray in the glass is incident on the interface. When the liquid is a certain alcohol, the incident ray arrives at the interface at the critical angle. The index of refraction of the alcohol is closest to: O A. 1.13 OB. 1.17 O C. 1.15 O D. 1.11

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Mergus Mergus · Answer 1 · 2019-08-28T05:00:47+02:00

Answer:

C. 1.15

Explanation:

The formula for the critical angle is:

[tex]{sin\theta_{critical}}=\frac {n_r}{n_i}[/tex]

Where,

[tex]{\theta_{critical}}[/tex] is the critical angle

[tex]n_r[/tex] is the refractive index of the refractive medium. ( Alcohol , ? )

[tex]n_i[/tex] is the refractive index of the incident medium. ( Glass, 1.66 )

Critical angle = 44º

Applying in the formula as:

[tex]{sin\theta_{critical}}=\frac {1}{1.523}[/tex]

[tex]{sin\ 44^0}=\frac {n_r}{1.66}[/tex]

[tex]{n_r}=1.15[/tex]