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The refractive index of the material of lens are 1.56 and 1.53 for yellow and red colours of lignt respectively. If the foceal length of lens for yellow colour is 20 cm then calculate the focal length of lens for red colour.?
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Most Upvoted Answer
The refractive index of the material of lens are 1.56 and 1.53 for yel...
Given:
Refractive index of lens for yellow colour (n₁) = 1.56
Refractive index of lens for red colour (n₂) = 1.53
Focal length of lens for yellow colour (f₁) = 20 cm

To Find:
Focal length of lens for red colour (f₂)

Explanation:
The refractive index of a material determines how much the light bends when it passes through the material. The refractive index is different for different colors of light. The focal length of a lens also depends on the refractive index of the material.

Step 1: Calculate the Lens Power:
The lens power (P) is given by the formula:
P = 1/f

where f is the focal length of the lens.

For the yellow color:
P₁ = 1/f₁ = 1/20 cm

Step 2: Calculate the Lens Power for Red Color:
Since the refractive index for red color is lower than that for yellow color, the lens power for red color will be higher than that for yellow color.

The lens power for red color (P₂) can be calculated using the formula:
P₂ = (n₁ - n₂)/f₂

where n₁ is the refractive index for yellow color, n₂ is the refractive index for red color, and f₂ is the focal length of the lens for red color.

Step 3: Calculate the Focal Length for Red Color:
We can rearrange the formula for lens power to solve for f₂:

P₂ = (n₁ - n₂)/f₂
f₂ = (n₁ - n₂)/P₂

Substituting the values:
f₂ = (1.56 - 1.53)/(1/20 cm)

Step 4: Calculate the Focal Length in cm:
Calculating the above expression gives:
f₂ = (0.03)/(1/20 cm)
f₂ = 0.03 * 20 cm
f₂ = 0.6 cm

Hence, the focal length of the lens for red color is 0.6 cm.
Community Answer
The refractive index of the material of lens are 1.56 and 1.53 for yel...
21.13 cm
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Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring material, then by Snell’slaw,it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation,n= c /where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and permeability of the medium respectively.In normal materials, both εr and μr , are positive, implying positive n for the medium. When both εr and μr are negative, one must choose the negative root of n. Such negative refractive index materials can now be artificially prepared and are called metamaterials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light.However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials. Q.Choose the correct statement.

Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring material, then by Snell’slaw,it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation,n= c /where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity and permeability of the medium respectively.In normal materials, both εr and μr , are positive, implying positive n for the medium. When both εr and μr are negative, one must choose the negative root of n. Such negative refractive index materials can now be artificially prepared and are called metamaterials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light.However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials. Q.For light incident from air on a meta-material, the appropriate ray diagram is

Paragraph for Questions 13 and 14Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurringmaterial, then by Snell’s law, it is understood that the refracted ray bends towards the normal.But it never emerges on the same side of the normal as the incident ray. According to electromagnetism,the refractive index of the medium is given by the relation, where c is the speed ofelectromagnetic waves in vacuum, v its speed in the medium, εr and μr are the relative permittivity andpermeability of the medium respectively.In normal materials, both εr and μr, are positive, implying positive n for the medium. When both εr and μrare negative, one must choose the negative root of n. Such negative refractive index materials can nowbe artificially prepared and are called meta-materials. They exhibit significantly different optical behavior,without violating any physical laws. Since n is negative, it results in a change in the direction ofpropagation of the refracted light. However, similar to normal materials, the frequency of light remainsunchanged upon refraction even in meta-materials.Q.Choose the correct statement.

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The refractive index of the material of lens are 1.56 and 1.53 for yellow and red colours of lignt respectively. If the foceal length of lens for yellow colour is 20 cm then calculate the focal length of lens for red colour.?
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