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One face of a rectangular glass plate of 8cm thickness is silvered. An object held 10cm in front of the unsilvered face forms an image 12cm behind the silvered face.What is the refractive index of the glass ?
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Most Upvoted Answer
One face of a rectangular glass plate of 8cm thickness is silvered. An...
Thickness of glass plate (t)= 6cm 
Distance of the image (u)= 8cm
And distance of the image (v)= 12cm
Let x= Apparent position of the slivered surface in cm 
Since the image is formed from due to reflection at the silvered face and by the property of the mirror image 
Distance of object from the mirror =Distance of image from the mirror 
or, x+8 =12+6-x 
x = 5cm 
Therefore, refractive index of glass = Real depth/ apparent depth =6�5=1.2
Community Answer
One face of a rectangular glass plate of 8cm thickness is silvered. An...
Problem Statement:
A rectangular glass plate with a thickness of 8cm has one face silvered. An object is placed 10cm in front of the unsilvered face, and an image is formed 12cm behind the silvered face. We need to determine the refractive index of the glass.

Solution:

Step 1: Understand the Problem
We are given a glass plate with one face silvered. The object is placed in front of the unsilvered face, and an image is formed behind the silvered face. We need to find the refractive index of the glass based on this information.

Step 2: Identify Given Information
- Thickness of the glass plate (t): 8cm
- Distance of the object from the unsilvered face (u): 10cm
- Distance of the image from the silvered face (v): 12cm

Step 3: Identify Relevant Concepts
To solve this problem, we need to use the concept of refraction and the lens formula.

The lens formula is given by:
1/f = 1/v - 1/u

Where:
- f is the focal length of the lens
- v is the distance of the image from the lens
- u is the distance of the object from the lens

Step 4: Apply the Concepts
Since the glass plate is silvered on one face, it acts as a lens. The refractive index of the glass (μ) can be determined using the lens formula.

We know that the thickness of the glass plate is 8cm. The distance from the unsilvered face to the silvered face is the sum of the distance of the object from the unsilvered face (u) and the distance of the image from the silvered face (v). Therefore, the total distance between the unsilvered and silvered faces is (u + v).

Using the lens formula, we can write:
1/f = 1/v - 1/u

Substituting the values, we have:
1/f = 1/12 - 1/10

Simplifying the equation gives:
1/f = (10 - 12) / (12 * 10)
1/f = -1/120

Since the object is placed in front of the unsilvered face, the focal length (f) is negative. Therefore, we can rewrite the equation as:
-1/f = 1/120

The refractive index (μ) of the glass can be calculated as:
μ = 1 + 1/f

Substituting the value of f, we get:
μ = 1 - 120
μ = -119

Step 5: Evaluate the Result
The refractive index of the glass is calculated to be -119. However, the refractive index cannot be negative. Therefore, there might be an error in the problem statement or the calculations. Please double-check the given information and calculations to ensure accuracy.
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Read the following text and answer the following questions on the basis of the same:Negative Refractive Index: One of the most fundamental phenomena in optics is refraction. When a beam of light crosses the interface between two different materials, its path is altered depending on the difference in the refractive indices of the materials. The greater the difference, the greater the refraction of the beam. For all known naturally occurring materials the refractive index assumes only positive values. But does this have to be the case?In 1967, Soviet physicist Victor Veselago hypothesized that a material with a negative refractive index could exist without violating any of the laws of physics.Veselago predicted that this remarkable material would exhibit a wide variety of new optical phenomena. However, until recently no one had found such a material and Veselago’s ideas had remained untested. Recently, meta-material samples are being tested for negative refractive index. But the experiments show significant losses and this could be an intrinsic property of negativeindex materials.Snell’s law is satisfied for the materials having a negative refractive index, but the direction of the refracted light ray is ‘mirror-imaged’ about the normal to the surface.There will be an interesting difference in image formation if a vessel is filled with “negative water” having refractive index – 1.33 instead of regular water having refractive index 1.33.Say, there is a fish in a vessel filled with negative water. The position of the fish is such that the observer cannot see it due to normal refraction since the refracted ray does not reach to his eye.But due to negative refraction, he will be able to see it since the refracted ray now reaches his eye.Q. A ray incident on normal glass and “negative glass” at an angle 60°. If the magnitude of angle of refraction in normal glass is 45° then, what will be the magnitude of angle of refraction in the “negative glass”?

Read the following text and answer the following questions on the basis of the same:Negative Refractive Index: One of the most fundamental phenomena in optics is refraction. When a beam of light crosses the interface between two different materials, its path is altered depending on the difference in the refractive indices of the materials. The greater the difference, the greater the refraction of the beam. For all known naturally occurring materials the refractive index assumes only positive values. But does this have to be the case?In 1967, Soviet physicist Victor Veselago hypothesized that a material with a negative refractive index could exist without violating any of the laws of physics.Veselago predicted that this remarkable material would exhibit a wide variety of new optical phenomena. However, until recently no one had found such a material and Veselago’s ideas had remained untested. Recently, meta-material samples are being tested for negative refractive index. But the experiments show significant losses and this could be an intrinsic property of negativeindex materials.Snell’s law is satisfied for the materials having a negative refractive index, but the direction of the refracted light ray is ‘mirror-imaged’ about the normal to the surface.There will be an interesting difference in image formation if a vessel is filled with “negative water” having refractive index – 1.33 instead of regular water having refractive index 1.33.Say, there is a fish in a vessel filled with negative water. The position of the fish is such that the observer cannot see it due to normal refraction since the refracted ray does not reach to his eye.But due to negative refraction, he will be able to see it since the refracted ray now reaches his eye.Q. Which of the following is the intrinsic property of negative-index materials?

One face of a rectangular glass plate of 8cm thickness is silvered. An object held 10cm in front of the unsilvered face forms an image 12cm behind the silvered face.What is the refractive index of the glass ?
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