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Chapter 37: Problem 2904

Light travels through a glass plate of thickness \(t\) and having refractive index \(\mathrm{n}\). If \(\mathrm{C}\) be the velocity of light in vacuum. What is the time taken by the light of travel this thickness of glass? (A) \(\left(\mathrm{t}_{\mathrm{C}} / \mathrm{n}\right)\) (B) \(\operatorname{tn} \mathrm{C}\) (C) (nt / C) (D) \((\mathrm{t} / \mathrm{n} \mathrm{C})\)

Short Answer

Expert verified
The time taken by the light to travel through the glass plate is \(t_{light} = \frac{nt}{C}\).

Step by step solution

01

Formulate the speed of light inside the glass:

We know the speed of light in a vacuum (C) and the refractive index of the glass (n). Recall the formula connecting speed of light and refractive index: \(v = \frac{C}{n}\), where v is the speed of light in the glass. This formula gives the speed of light inside the glass.
02

Use the speed-distance-time formula:

To find the time taken by the light to travel through the glass plate of thickness t, we can use the formula: \(t_{light} = \frac{d}{v}\), where \(t_{light}\) is the time taken by the light, d is the distance traveled (i.e., the thickness of the glass plate), and v is the speed of light inside the glass.
03

Substitute values in the formula:

Now, we can substitute the values of d, and v from the previous steps: \(t_{light} = \frac{t}{\frac{C}{n}}\).
04

Simplify to find the time taken:

When we simplify the expression, we get: \(t_{light} = \frac{t * n}{C}\). Comparing with the given options, the answer is (C) (nt / C).

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Most popular questions from this chapter

A vessel of depth \(\mathrm{t}\) is half filled with oil of refractive index \(\mathrm{n}_{1}\) and the other half is filled with water (refractive index \(\mathrm{n}_{2}\) ). The apparent depth of the vessel when viewed from above is \(\ldots \ldots\) (A) $\left[\left\\{2 t\left(n_{1}-\mathrm{n}_{2}\right)\right\\} /\left(\mathrm{n}_{1} \mathrm{n}_{2}\right)\right]$ (B) $\left[\left\\{2 \mathrm{t}\left(\mathrm{n}_{1}+\mathrm{n}_{2}\right)\right\\} /\left(\mathrm{n}_{1} \mathrm{n}_{2}\right)\right]$ (C) $\left[\left\\{t\left(n_{1}-n_{2}\right)\right\\} /\left(2 n_{1} \mathrm{n}_{2}\right)\right]$ (D) $\left[\left\\{t\left(n_{1}+n_{2}\right)\right\\} /\left(2 n_{1} \mathrm{n}_{2}\right)\right]$

A bird in air looks at a fish vertically below it and inside water, \(h_{1}\) is the height of the bird above the surface of water and \(\mathrm{h}_{2}\), the depth of the fish below the surface of water. If refractive index of water with respect to air be \(\mathrm{n}\), then what is the distance of the fish observed by the bird? (A) \(\mathrm{n}_{1} \mathrm{~h}_{1}+\mathrm{nh}_{2}\) (B) \(\mathrm{nh}_{1}+\mathrm{h}_{2}\) (C) \(\mathrm{h}_{1}+\left(\mathrm{h}_{2} / \mathrm{n}\right)\) (D) \(\mathrm{h}_{1}+\mathrm{h}_{2}\)

A beam of light is converging towards a point I on a screen. A plane parallel plate of glass whose thickness is in the direction of beam \(=\mathrm{t}\), refractive index \(=\mathrm{n}\) is introduced in the path of the beam. The convergence point is shifted by \(\ldots \ldots\) (A) \(t[1+(1 / n)]\) never (B) \(t[1-(1 / n)]\) nearer (C) \(\mathrm{t}[1+(1 / \mathrm{n})]\) away (D) \(t[1-(1 / n)]\) away

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index \(\mathrm{n} . \mathrm{P}\) is a small object at a height \(\mathrm{h}\) above the mirror. An observer O, vertically above P, outside the liquid sees \(\mathrm{P}\) and its image in the mirror. The apparent distance between these two will be. (A) \((2 \mathrm{~h} / \mathrm{n})\) (B) \(2 \mathrm{~h}(\mathrm{n}-1)\) (C) \(h[1+(1 / n)]\) (D) \((2 \mathrm{n} / \mathrm{h})\)

The velocity of light in glass whose refractive index with respect to air is \(1.5\) is \(2 \times 10^{8} \mathrm{~m} / \mathrm{s}\). In a certain liquid, the velocity of light is found to be \(2.5 \times 10^{8} \mathrm{~m} / \mathrm{s}\). What is the refractive index of the liquid with respect to air? (A) \(1.44\) (B) \(0.80\) (C) \(1.20\) (D) \(0.64\)
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