Question

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

Answer 1

Answer:

1.5

Explanation:

Let the refractive index of medium be η. The thickness of glass slab is 6 cm. But due to refraction, the appeared thickness would be different

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.Also the appeared distance of the image from silvered surface would be (6−x+10) cm=(16−x) cm.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.Also the appeared distance of the image from silvered surface would be (6−x+10) cm=(16−x) cm.By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.Also the appeared distance of the image from silvered surface would be (6−x+10) cm=(16−x) cm.By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.Thus, 8+x=16−x.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.Also the appeared distance of the image from silvered surface would be (6−x+10) cm=(16−x) cm.By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.Thus, 8+x=16−x.Solving the equation above, we get, x=4 cm.

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.Also the appeared distance of the image from silvered surface would be (6−x+10) cm=(16−x) cm.By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.Thus, 8+x=16−x.Solving the equation above, we get, x=4 cm.As, η=

So the appeared distance of object from the silvered face (which acts as a plane mirror) would be (8+x) cm.Also the appeared distance of the image from silvered surface would be (6−x+10) cm=(16−x) cm.By law of reflection from plane mirror, distance of the object from mirror is equal to the distance of image from the mirror.Thus, 8+x=16−x.Solving the equation above, we get, x=4 cm.As, η= Distance in vacuum air/Distance in material

= 6/4

=1.5

=1.5

So the refractive index of the glass is equal to 1.5

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