Question

The light beam shown in the figure below makes an angle of? = 15.5° with the normal line NN' in the linseedoil. Determine the angles θ and θ'.(The refractive index for linseed oil is 1.48.)

θ = 1
°
θ' = 2
°

Answer 1

To determine the angles θ and θ' in linseed oil, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the media involved. The angle θ' is found to be approximately 9.9° and the angle θ is approximately 80.1°.

Step-by-step explanation:

To determine the angles θ and θ', we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the media involved. Snell's law is given by:

n₁sinθ₁ = n₂sinθ₂

Where n₁ is the refractive index of the initial medium, n₂ is the refractive index of the final medium, θ₁ is the angle of incidence, and θ₂ is the angle of refraction.

In this case, the initial medium is air with a refractive index of 1, and the final medium is linseed oil with a refractive index of 1.48. The angle of incidence is given as 15.5°. Plugging these values into Snell's law:

1 x sin15.5° = 1.48 x sinθ₂

Solving for θ₂, we find that θ₂ is approximately 9.9°.

Since the angles in the figure are complementary, we can find θ using:

θ = 90° - θ₂
θ = 90° - 9.9°
θ ≈ 80.1°

Therefore, the angles are:

θ ≈ 80.1°
θ₂ ≈ 9.9°

Answer 2

To determine the index of refraction of the unknown substance, Snell's law is applied using the given incident angle and observed angle of refraction. By performing the calculations, the index of refraction is found to be approximately 1.43, which could indicate the substance is a type of glass or plastic.

Step-by-step explanation:

To find the index of refraction of the unknown substance using the information provided (incident angle of 45.0° and the angle of refraction of 40.3° in water), we need to apply Snell's law, which states:

n1 · sin(θ1) = n2 · sin(θ2)

Where:

• n1 is the refractive index of water (1.33)
• θ1 is the incident angle in water (45.0°)
• θ2 is the angle of refraction in the substance (40.3°)

and n2 is the refractive index of the unknown substance, which is what we're solving for.

Plugging our known values into Snell's law:

1.33 · sin(45.0°) = n2 · sin(40.3°)

First, calculate the sine of both angles:

sin(45.0°) = 0.7071

sin(40.3°) = 0.6561

Now, plug the sine values into Snell's law and solve for n2:

1.33 · 0.7071 = n2 · 0.6561

0.9394 = n2 · 0.6561

Dividing both sides by 0.6561 gives us:

n2 = 0.9394 / 0.6561 ≈ 1.43

The index of refraction of the substance is approximately 1.43, which could suggest the substance is a certain type of glass or plastic.