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Chapter 23: Problem 93

A glass block \((n=1.7)\) is submerged in an unknown liquid. A ray of light inside the block undergoes total internal reflection. What can you conclude concerning the index of refraction of the liquid?

Short Answer

Expert verified
Answer: The index of refraction of the unknown liquid must be less than 1.7.

Step by step solution

01

Understand Total Internal Reflection

Total internal reflection occurs when a ray of light passes from a denser medium (higher refractive index) to a less dense medium (lower refractive index) and the angle of incidence is greater than the critical angle. This results in the complete reflection of the light back into the denser medium.
02

Write down the condition for Total Internal Reflection

For total internal reflection to occur, the incident angle must be greater than the critical angle. The critical angle is given by Snell's law: \[\sin(\theta_c) = \frac{n_2}{n_1}\] Where \(\theta_c\) is the critical angle, \(n_1\) is the index of refraction of the denser medium (glass block in our case), and \(n_2\) is the index of refraction of the less dense medium (the unknown liquid).
03

Evaluate the condition for the unknown liquid's refractive index

Since the light undergoes total internal reflection, we can conclude that the index of refraction of the liquid must be less than that of the glass block. Mathematically, this means: \[n_2 < n_1\] With the given information, we know that the index of refraction of the glass block is 1.7, so the condition becomes: \[n_2 < 1.7\]
04

Conclude the refractive index of the unknown liquid

From the analysis, we can conclude that the index of refraction of the unknown liquid must be less than 1.7 for total internal reflection to occur within the glass block.

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Most popular questions from this chapter

An object \(8.0 \mathrm{cm}\) high forms a virtual image \(3.5 \mathrm{cm}\) high located \(4.0 \mathrm{cm}\) behind a mirror. (a) Find the object distance. (b) Describe the mirror: is it plane, convex, or concave? (c) What are its focal length and radius of curvature?
In her job as a dental hygienist, Kathryn uses a concave mirror to see the back of her patient's teeth. When the mirror is \(1.20 \mathrm{cm}\) from a tooth, the image is upright and 3.00 times as large as the tooth. What are the focal length and radius of curvature of the mirror?
Show that the deviation angle \(\delta\) for a ray striking a thin converging lens at a distance \(d\) from the principal axis is given by \(\delta=d l f .\) Therefore, a ray is bent through an angle \(\delta\) that is proportional to \(d\) and does not depend on the angle of the incident ray (as long as it is paraxial). [Hint: Look at the figure and use the small-angle approximation \(\sin \theta=\tan \theta \approx \theta(\text { in radians) } .]\)
A beam of light in air is incident on a stack of four flat transparent materials with indices of refraction 1.20 \(1.40,1.32,\) and \(1.28 .\) If the angle of incidence for the beam on the first of the four materials is \(60.0^{\circ},\) what angle does the beam make with the normal when it emerges into the air after passing through the entire stack?
A concave mirror has a radius of curvature of \(5.0 \mathrm{m} .\) An object, initially \(2.0 \mathrm{m}\) in front of the mirror, is moved back until it is \(6.0 \mathrm{m}\) from the mirror. Describe how the image location changes.
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