To determine the refractive index of a thin transparent wedge illuminated by monochromatic light with a wavelength of 0.48 μm, incident normally on its surface and having a distance b between adjacent interference maxima in reflected light equal to 0.32 mm, you can use the following calculation formula:
n = (b * λ) / (2 * t * cosθ)
Where n is the desired refractive index, λ is the wavelength of light, t is the thickness of the wedge, θ is the angle of incidence of light on the wedge.
To find the angle θ, you can use the law of light refraction: n1 * sinθ1 = n2 * sinθ2, where n1 and n2 are the refractive indices of the medium from which the light comes and the medium in which it propagates, respectively.
When light is normally incident on the wedge, the angle θ will be zero, so sinθ1 = 0 and sinθ2 = n1/n2.
Thus, the formula for calculating the refractive index of a wedge will take the form:
n = (b * λ) / (2 * t * n1/n2)
Substituting numerical values, we get:
n = (0.32 mm * 0.48 μm) / (2 * t * 1)
Considering that a thin wedge is considered thin if its thickness t is much less than the wavelength of light, we can assume t = 0.
Thus, the required refractive index is equal to:
n = 0,32 / 2 = 0,16
Answer: n = 0.16.
We present to your attention a digital product that will help you solve the problem of determining the refractive index of a thin transparent wedge illuminated by monochromatic light with a wavelength of 0.48 μm incident normally on its surface, provided that the distance between adjacent interference maxima in the reflected light is 0 .32 mm.
Our digital product contains a detailed solution to the problem with a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. We are confident that this product will help you quickly and easily solve this problem and significantly save your time and effort.
Our product is available for download at any time and place convenient for you. You can download it from our website after payment and start using it immediately. If you have any questions about using a product or solving a problem, our technical support team is always ready to help you.
We present to your attention a digital product that will help you solve the problem of determining the refractive index of a thin transparent wedge illuminated by monochromatic light with a wavelength of 0.48 μm incident normally on its surface, provided that the distance between adjacent interference maxima in the reflected light is 0 .32 mm.
Our digital product contains a detailed solution to the problem with a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer. Using the formula n = (b * λ) / (2 * t * n1/n2) and taking into account that a thin wedge is considered thin if its thickness t is much less than the wavelength of light, we get the desired answer: n = 0.16.
We are confident that this product will help you quickly and easily solve this problem and significantly save your time and effort. Our product is available for download at any time and place convenient for you. If you have any questions about using a product or solving a problem, our technical support team is always ready to help you.
We present to your attention a digital product that will help you solve the problem of determining the refractive index of a thin transparent wedge illuminated by monochromatic light with a wavelength of 0.48 μm incident normally on its surface, provided that the distance between adjacent interference maxima in the reflected light is 0 .32 mm.
This digital product contains a detailed solution to the problem, including a brief condition, formulas and laws used in the solution, derivation of the calculation formula and the answer. To determine the refractive index of a thin transparent wedge, you can use the formula:
n = (b * λ) / (2 * t * n1/n2)
where n is the desired refractive index, λ is the wavelength of light, t is the thickness of the wedge, b is the distance between adjacent interference maxima in reflected light, n1 and n2 are the refractive indices of the medium from which the light comes and the medium in which it propagates, respectively .
Considering that a thin wedge is considered thin if its thickness t is much less than the wavelength of light, we can assume t = 0. When light is normally incident on the wedge, the angle θ will be zero, so sinθ1 = 0 and sinθ2 = n1/n2.
Thus, the required refractive index is equal to:
n = (b * λ) / (2 * t * n1/n2)
n = (0.32 mm * 0.48 μm) / (2 * 0 * 1)
Answer: n = 0.16.
Our digital product is available for download at any time and place convenient for you. You can download it from our website after payment and start using it immediately. If you have any questions about using a product or solving a problem, our technical support team is always ready to help you.
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This product is a solution to problem 40589, which involves determining the refractive index of a thin transparent wedge.
The problem statement states that the wedge is illuminated by monochromatic light with a wavelength of 0.48 μm, which is incident normally on the surface of the wedge. The distance between adjacent interference maxima in reflected light is 0.32 mm.
To solve the problem, it is necessary to use the laws of light interference and the relationship between the refractive indices of a prism and its angle of inclination.
The calculation formula for determining the refractive index of a wedge is:
n = (b * λ) / (2 * t * cosθ)
where n is the desired refractive index, λ is the wavelength of light, b is the distance between adjacent interference maxima in reflected light, t is the thickness of the wedge, θ is the angle of inclination of the wedge.
To solve the problem, it is necessary to take into account that a thin wedge is a prism with an apex angle equal to zero, therefore the angle of inclination of the wedge θ is also equal to zero.
Thus, to determine the refractive index of a wedge, it is necessary to know only the distance between adjacent interference maxima in reflected light and the thickness of the wedge.
After substituting the known values into the calculation formula and carrying out the necessary calculations, we will obtain the desired refractive index of the wedge.
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