Question

The refractive index of vegetable oil is 1.47. A ray of light enters a drop of vegetable oil and is refracted by 12°. At what angle did the ray of light enter the drop? Give your answer to the nearest degree.

Answer 1

The refraction's law allows to find the result for the angle of incidence of the light ray is:

• The incident angle is: θ = 18º

Law of refraction.

Geometric optics studies the movement of light using its geometric properties, it is described by two laws:

• Reflection. They indicate that the angle of incidence is equal to the angle of reflection of light.

• Refraction. It is used for the transmission of light through various media and is expressed by the ratio.

               $n_1 \ sin \theta_1 = n_2 \ sin \theta_2$

Where the subscripts 1 and 2 are for the incident and refracted media, respectively, n is the refractive index and θ is the angle with respect to the normal of the media.

In the attachment we can see a system diagram, where the incident medium is the air with a refaction index n₁ = 1 and the transmitted medium has an index n₂ = 1.47 and the angle of this medium is θ₂= 12º

              $sin \theta_1 = \frac{n_2}{n_1} \ sin \theta_2$

Let's calculate.

             $sin \theta_1 = \frac{1.47}{1} \ sin 12 = \ 0.3056$

            $\theta_1 = sin^{-1} \ 0.3056$

            θ₁ = 17.8º

They ask for the approximate answer to degrees, therefore using the criterion of significant figures:

• If the number following the figure to approximate is greater than or equal to 5, the figure is increased by one unit.

• If it is less than 5, it is left the same.

The result for the incident angle, using the test of significant figures is:

            θ = 18º

in conclusion using the refraction's law we can find the result for the angle of incidence of light ray is:

• The incident angle is: θ = 18º

Learn more about the refraction's law here:  brainly.com/question/16050768