Ray Optics and Optical Instruments
Refraction through a glass slab
- Definition: Refraction is the bending of light when it travels from one medium to another medium.
- Refractive Index (n): Ratio of the speed of light in vacuum to the speed of light in a medium.
- Snell’s Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the refractive index.
- Formula for Snell’s Law: n₁ sin(θ₁) = n₂ sin(θ₂)
- Total Internal Reflection: When light is incident from a denser medium to a rarer medium at an angle greater than the critical angle, it is totally reflected back into the denser medium.
- Critical Angle (θc): The angle of incidence for which the angle of refraction is 90 degrees.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Refraction through a glass slab can be understood using the principles of refraction.
- When light passes through a glass slab, it undergoes refraction twice – once at the entry surface and once at the exit surface of the slab.
- The incident ray, refracted ray, and the normal at both the surfaces lie in the same plane.
- The deviation produced by a glass slab depends on the refractive index of the glass and the angle of incidence.
- The lateral shift (displacement) produced by a glass slab can be calculated using the formula: D = t (μ - 1) α
- D: Lateral shift or displacement
- t: Thickness of the glass slab
- μ: Refractive index of the glass
- α: Angle of incidence
Ray Optics and Optical Instruments
Refraction through a glass slab
- The lateral shift is directly proportional to the thickness of the slab, angle of incidence, and refractive index.
- If the angle of incidence is zero, there will be no lateral shift.
- The lateral shift is maximum when the angle of incidence is 90 degrees.
- The lateral shift increases with an increase in the thickness of the glass slab.
- The direction of the lateral shift depends on the orientation of the glass slab with respect to the incident ray.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example: Light is incident normally on a glass slab (θ₁ = 0 degrees).
- The lateral shift is given by D = t (μ - 1) α.
- As the angle of incidence is zero, the lateral shift is also zero.
- Example: Light is incident at an angle of 60 degrees on a glass slab of refractive index 1.5.
- The lateral shift can be calculated using the formula D = t (μ - 1) α.
Ray Optics and Optical Instruments
Refraction through a glass slab
- The refractive index of a medium depends on the wavelength of light.
- The refractive index of a medium is different for different colors of light, leading to dispersion.
- Dispersion: The phenomenon of separating white light into its constituent colors.
- The refractive index of a medium is highest for violet light and lowest for red light.
- The angle of refraction is different for different colors when passing through a prism, leading to the formation of a spectrum.
Ray Optics and Optical Instruments
Refraction through a glass slab
- The lateral shift produced by a glass slab is independent of the color of light passing through it.
- However, the angles of incidence and refraction vary for different colors, leading to dispersion.
- The phenomenon of dispersion is utilized in the formation of a spectrum in various optical devices.
- Examples of optical devices utilizing dispersion: Prism, spectrometer, rainbow formation, etc.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Application: Glass slabs are used in optical devices to redirect and control the path of light.
- Prism: A triangular glass slab that refracts light and produces a spectrum.
- Spectrometer: An instrument that uses a prism to separate and analyze the colors of light.
- Optical fibers: Long, thin strands of glass that transmit light through total internal reflection.
- Thick lenses: Used in spectacles and camera lenses to correct vision problems and focus light.
- These applications rely on the properties of refraction and the behavior of light passing through glass slabs.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Summary:
- Refraction is the bending of light when it travels from one medium to another.
- Snell’s Law relates the angles of incidence and refraction to the refractive index.
- Refraction through a glass slab occurs twice, leading to a lateral shift.
- The lateral shift depends on the thickness, angle of incidence, and refractive index.
- Dispersion is the separation of white light into its constituent colors due to different refractive indices.
- Optical devices like prism and spectrometer use refraction and dispersion for various applications.
Slide 11
- Recap:
- Refraction is the bending of light when it travels from one medium to another.
- Snell’s Law relates the angles of incidence and refraction to the refractive index.
- Refraction through a glass slab occurs twice, leading to a lateral shift.
- The lateral shift depends on the thickness, angle of incidence, and refractive index.
- Dispersion is the separation of white light into its constituent colors due to different refractive indices.
Slide 12
- Example 1: Light enters a glass slab (μ = 1.5) with an angle of incidence of 30 degrees. Calculate the angle of refraction.
- Solution: Using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂), we have sin(θ₂) = (n₁ / n₂) * sin(θ₁)
- Plugging in the values, sin(θ₂) = (1 / 1.5) * sin(30°) = 0.577 * 0.5 = 0.2888
- Taking the inverse sine of 0.2888, we get θ₂ ≈ 17.54°.
Slide 13
- Example 2: A light ray passes through a glass slab (μ = 1.6) at an angle of incidence of 45 degrees. Calculate the angle of refraction.
- Solution: Using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂), we have sin(θ₂) = (n₁ / n₂) * sin(θ₁)
- Plugging in the values, sin(θ₂) = (1 / 1.6) * sin(45°) = 0.625 * 0.7071 = 0.4418
- Taking the inverse sine of 0.4418, we get θ₂ ≈ 26.8°.
Slide 14
- Example 3: A light ray enters a glass slab (μ = 1.8) at an angle of incidence of 60 degrees. Calculate the angle of refraction.
- Solution: Using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂), we have sin(θ₂) = (n₁ / n₂) * sin(θ₁)
- Plugging in the values, sin(θ₂) = (1 / 1.8) * sin(60°) = 0.556 * 0.866 = 0.481
- Taking the inverse sine of 0.481, we get θ₂ ≈ 29.1°.
Slide 15
- Example 4: A light ray enters a glass slab (μ = 1.5) parallel to the base of the slab. Calculate the angle of refraction.
- Solution: When the light ray enters parallel to the base, the angle of incidence is 90 degrees. The angle of refraction can be calculated using Snell’s Law, sin(θ₂) = (n₁ / n₂) * sin(θ₁)
- Plugging in the values, sin(θ₂) = (1 / 1.5) * sin(90°) = 0.667 * 1 = 0.667
- Taking the inverse sine of 0.667, we get θ₂ ≈ 41.81°.
Slide 16
- Recap:
- Refraction can be described using Snell’s Law: n₁ sin(θ₁) = n₂ sin(θ₂)
- Examples were provided to calculate the angle of refraction in different scenarios.
- The angle of refraction depends on the refractive indices and the angle of incidence.
- When the angle of incidence is 90 degrees, the angle of refraction can be calculated as sin(θ₂) = (n₁ / n₂).
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example 5: A glass slab (μ = 1.5) of thickness 2 cm is placed in air (μ = 1). A light ray enters the slab at an angle of incidence of 45 degrees. Calculate the lateral shift.
- Solution: The lateral shift can be calculated using the formula D = t (μ - 1) α.
- Plugging in the values, D = 0.02 m (1.5 - 1) 45° ≈ 0.3 m.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example 6: A glass slab (μ = 1.6) is immersed in a medium with a refractive index of 1.3. A light ray enters the slab at an angle of incidence of 30 degrees. Calculate the angle of refraction in the medium.
- Solution: Using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂), we have sin(θ₂) = (n₁ / n₂) * sin(θ₁).
- Plugging in the values, sin(θ₂) = (1.6 / 1.3) * sin(30°) ≈ 1.231 * 0.5 = 0.616.
- Taking the inverse sine of 0.616, we get θ₂ ≈ 38.04°.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example 7: A light ray passes through a glass slab (μ = 1.4) at an angle of incidence of 60 degrees and undergoes a lateral shift of 0.08 m. Calculate the thickness of the slab.
- Solution: Rearranging the lateral shift formula, we have t = D / ((μ - 1) α).
- Plugging in the values, t = 0.08 m / ((1.4 - 1) 60°) ≈ 1.43 m.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example 8: A glass slab is immersed in water (μ = 1.33). A light ray enters the slab at an angle of incidence of 45 degrees. Calculate the angle of refraction in water.
- Solution: Using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂), we have sin(θ₂) = (n₁ / n₂) * sin(θ₁).
- Plugging in the values, sin(θ₂) = (1.5 / 1.33) * sin(45°) ≈ 1.128 * 0.7071 = 0.797.
- Taking the inverse sine of 0.797, we get θ₂ ≈ 53.5°.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example 9: A light ray passes through a glass slab. The angle of incidence is twice the angle of refraction. Calculate the refractive index of the medium.
- Solution: Using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂), we can write the given condition as θ₁ = 2θ₂.
- Substituting the equation into Snell’s Law, n₁ sin(2θ₂) = n₂ sin(θ₂).
- Rearranging the equation, n₂ / n₁ = sin(2θ₂) / sin(θ₂) = 2 cos(θ₂).
- As θ₂ is the angle of incidence and θ₁ is the angle of refraction, n₂ / n₁ = 2 cos(θ₁).
- Therefore, the refractive index of the medium is 2 cos(θ₁).
Ray Optics and Optical Instruments
Refraction through a glass slab
- Example 10: A glass slab (μ = 1.5) is placed in a medium with a refractive index of 1.33. Calculate the angle of incidence at which the light ray will emerge parallel to the base of the slab.
- Solution: When the light ray emerges parallel to the base, the angle of refraction is 90 degrees. The angle of incidence can be calculated using Snell’s Law, n₁ sin(θ₁) = n₂ sin(θ₂).
- Plugging in the values, sin(90°) = (1.5 / 1.33) * sin(θ₁).
- Simplifying the equation, 1 = (1.5 / 1.33) * sin(θ₁) ≈ 1.128 * sin(θ₁).
- Taking the inverse sine of 1 / 1.128, we get θ₁ ≈ 87°.
Ray Optics and Optical Instruments
Refraction through a glass slab
- Summary:
- Examples were provided to calculate the lateral shift, angle of refraction, thickness of the slab, and refractive index in various scenarios.
- Equations such as D = t (μ - 1) α, n₁ sin(θ₁) = n₂ sin(θ₂), and n₂ / n₁ = 2 cos(θ₁) were used in solving the problems.
- Understanding the behavior of light passing through a glass slab is essential for various optical applications.