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(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 41.3 angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2 from the normal, what is the refractive index of the unknown liquid?

Short Answer

Expert verified
(a) The angle in methanol is approximately 29.8°. (b) The refractive index of the unknown liquid is about 1.909.

Step by step solution

01

Understand the refraction through glass

For part (a), we have the refractive index of air as nair=1, refractive index of glass nglass=1.550, and the angle of incidence in air θ1=41.3. We need to find the angle of refraction θ2 in the glass using Snell's law: nairsinθ1=nglasssinθ2. Substitution gives:sinθ2=11.550sin(41.3).
02

Solve for the angle in the glass

Solving for θ2:sinθ2=11.550(0.6585)0.4249θ2=arcsin(0.4249)25.2. This is the angle of refraction in the glass.
03

Refraction from glass to methanol

Given the refractive index of methanol nmethanol=1.329. Use Snell's law again from glass to methanol:nglasssinθ2=nmethanolsinθ3where θ2=25.2 is the angle in the glass and we solve for θ3 in methanol:sinθ3=1.550×0.42491.3290.4962θ3=arcsin(0.4962)29.8.
04

Use given conditions for unknown liquid

For part (b), we have θ1=41.3 (incident angle) and θ4=20.2 (refracted angle into unknown liquid). Use Snell's law:nairsinθ1=nunknownsinθ4Subsitute known values and solve for nunknown:1sin(41.3)=nunknownsin(20.2)nunknown=0.65850.34501.909.
05

Conclusion

For part (a), the angle the light makes with the normal in the methanol is 29.8. For part (b), the refractive index of the unknown liquid is approximately 1.909.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Refractive Index
Refractive index is a crucial concept in optics. It indicates how much light bends, or refracts, when entering a different medium. The refractive index, denoted by the symbol "n," is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. This is expressed by the equation n=cvwhere "c" is the speed of light in a vacuum and "v" is the speed of light in the medium. A higher refractive index means light travels more slowly through the medium, resulting in a greater bending of the light. This property is essential when calculating how light behaves when entering or exiting materials like glass, water, or methanol.
Understanding the refractive index helps us use Snell's Law to predict the path of light in various mediums, making it invaluable in fields that involve optics, such as physics, biology, and even photography.
Angle of Incidence
The angle of incidence is the angle between the incoming light ray and the normal to the surface at the point of contact. In this context, "normal" means perpendicular to the surface. When a light ray strikes a boundary, the angle of incidence helps determine how much the light will reflect or refract. It is usually represented by the Greek letter θ with a subscript indicating its position, such as θ1 for the first medium.
  • When the angle of incidence is increased, the refraction angle is also likely to change, according to Snell’s Law.
  • An incident angle of 0° means the light hits the surface head-on, resulting in no bending.
In everyday examples like sunlight hitting a mirror or glass, understanding this angle helps us predict where the reflected or refracted light will go.
Angle of Refraction
The angle of refraction is the angle formed between the refracted ray and the normal to the surface at the point where the light passes into the new medium. It is determined using Snell's Law, which relates the sine of the angles of incidence and refraction to the refractive indices of the two media:n1sin(θ1)=n2sin(θ2)where n1 and n2 are the refractive indices of the initial and second medium, respectively, while θ1 and θ2 are the angles of incidence and refraction.
This equation is a core tool for predicting how light will behave as it travels between different materials. Knowing the angle of refraction is important in applications ranging from designing lenses to studying the behavior of light in different substances.
Optics
Optics is the branch of physics that studies light and its interactions with different objects. It encompasses a variety of phenomena, including reflection, refraction, and diffraction. These principles explain how light behaves under different circumstances and allow us to design practical applications such as cameras, glasses, and even lasers. In optics, understanding how light bends when passing through various materials is key. This bending, controlled by Snell's Law, is what allows lenses to focus light and for telescopes to magnify distant objects.
The broader field of optics ranges from simple lenses to complex structures like fiber optic cables used in telecommunications, making it essential for various technological advances.
Refraction in Mediums
Refraction is the bending of light as it passes from one medium into another due to a change in its speed. This principle is particularly important when different mediums have different refractive indices. For example, when light moves from air (with a refractive index of 1.0) into water (index of roughly 1.33), its speed decreases and the light ray bends toward the normal.
  • Refraction occurs because light changes speed as it travels between mediums with different densities.
  • This change in speed causes the light to bend, a phenomenon predicted accurately by Snell's Law.
  • Common examples of refraction include the bending of a straw when observed through a glass of water or the mirage effect on hot pavement.
Refraction is a critical concept in optics, helping us to design lenses and optical instruments that correct vision, concentrate light, and study tiny details in research.

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Most popular questions from this chapter

The indexes of refraction for violet light (λ=400nm) and red light (λ=700nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 53.5 to the normal. Calculate the angular separation between these two colors of light in the refracted ray.

In a physics lab, light with wavelength 490 nm travels in air from a laser to a photocell in 17.0 ns. When a slab of glass 0.840 m thick is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light 21.2 ns to travel from the laser to the photocell. What is the wavelength of the light in the glass?

A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a bucket. A ray of light from the bottom of the bucket travels upward through the water. (a) What is the largest angle with respect to the normal that the ray can make at the ice-water interface and still pass out into the air above the ice? (b) What is this angle after the ice melts?

The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina. What are the ranges of (a) the wavelength, (b) the frequency, and (c) the speed of the light just as it approaches the retina within the vitreous humor?

A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of θa=36.2, the ray refracted into the water makes an angle of 49.8 with the normal to the interface. What is the smallest value of the incident angle θa for which none of the ray refracts into the water?

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