Concept explainers
The
Answer to Problem 85QAP
The completed table is shown below.
Optical material with percentage of time required for light to pass through compared to an equal length of vacuum | Speed of light(meter/sec) | Index of refraction |
100% | | 1 |
125% | | 1.25 |
150% | | 1.5 |
200% | | 2 |
500% | | 5 |
1000% | | 10 |
Explanation of Solution
Given info:
The given table is shown below,
Optical material with percentage of time required for light to pass through compared to an equal length of vacuum | Speed of light(meter/sec) | Index of refraction |
100% | ||
125% | ||
150% | ||
200% | ||
500% | ||
1000% |
Formula used:
The speed of light in a given optical material can be expressed as the ratio of the time that is required for light to travel through a length of vacuum to the time required for light to travel through the same length of the optical material.
Time required for light to travel through a length of vacuum =
Time required for light to travel through the same length of optical material =
The ratio of time is,
The velocity of light in the optical medium is,
Refractive index of an optical material is calculated by using the following relation
Calculation:
For 100%,
Similarly,
The ratio is calculated for different percentage as shown below.
Optical material with percentage of time required for light to pass through compared to an equal length of vacuum | ||
100% | 1 | 1 |
125% | 1.25 | 0.8 |
150% | 1.5 | 0.67 |
200% | 2 | 0.5 |
500% | 5 | 0.2 |
1000% | 10 | 0.1 |
Now, the velocity of light in a material is,
The refractive index is,
So, for 100%,
Similarly, the speed as well as refractive index for different percentage is shown below.
Optical material with percentage of time required for light to pass through compared to an equal length of vacuum | Speed of light(meter/sec) | Index of refraction |
100% | | 1 |
125% | | 1.25 |
150% | | 1.5 |
200% | | 2 |
500% | | 5 |
1000% | | 10 |
Want to see more full solutions like this?
Chapter 23 Solutions
COLLEGE PHYSICS
- D) 2376 m/s During an Apollo moon landing, reflecting panels were placed on the moon. This allowed earth-based astronomers to shoot laser beams at the moon's surface to determine its distance. The reflected laser beam was observed 2.52 s after the laser pulse was sent. If the speed of light is 3.00x10 m/s, what was the distance between the astronomers and 10) the moon? A) 3.78x10 m B) 37800000 m 8.40x10 m D) 8.40x10 if you were the first Mars explorer and discovered that when you dropped a hammer if took 0.68 s to fall 0.90 m to the ground, what would you calculate for the gravitational acceleration on Mars? 11) A) 4.32x 10 m/sarrow_forward| W ▶ W File Paste 16° |×15° |·14°|•13° |·12·1·11·1·10·1·9·1·8·1·7·1·6·1·5·1·4·1·3·1·2·1·1·1·|··1·1·20 Home Insert Page Layout Cut Copy Format Painter Clipboard * l 0 08:43 PM 2022-08-23 Page: 1 of 1 Words: 11 Calibri (Body) T BIU 14 References T I U abe X₂ X³ abe X, X² Font Α Α΄ A Mailings B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbCc AaBI AaBbCcl Normal No Spaci... Heading 1 Title Subtitle Heading 2 Styles ··2·1·1·|*|*|·1·1·2·1·3·1·4·1·5·1·6·1·7· 1 · 8 · 1 ·9·|··10·|·11·|·12·|·13·|·14°|·15·| ·|\_\\ ·| ·17·| · 18 · T Aa ab Aal Document1 - Microsoft Word (Product Activation Failed) View F Review ATOMIC AND NUCLEAR PHYSICS Paragraph PLEASE HELP ANSWER ALL THE QUESTIONS BELOW: 3 (a) Using the Fermi gas model, calculate the energy of the lowest state for Thorium nucleus (Th). Hint: Use the nuclear radius R = R₁A¹/3, where Ro = 1.2 fm and A the atomic mass number. 2/3h²N5/3 +25/3 E G (3) ² 40 V2/3, where h is the Planck constant and m the atomic mass. m Consider the nucleus to be a sphere of…arrow_forwardQuestions If F = (2x - 32)i - 2xy j-4xk, then evaluate ff, V Fdv, where V is bounded by 1. x = 0, y = 0, z = 0 and 2x + 2y +z 4. 2. Evaluate |||, dV, where o = 45 xy and V is the closed region bounded by the planes 4x + 2y + z = 8, x = 0, y = 0, z = 0arrow_forward
- •48 In Fig. 33-48a, a light ray in water is incident at angle 61 on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction 6, versus the incident angle 6, is given in Fig. 33-48b. The vertical axis scale is set by 6, = 90°. %3D Without calculation, determine whether the index of refraction of (a) material 1 and (b) material 2 is greater or less than the index of water (n = 1.33). What is the index of refraction of (c) material 1 and (d) material 2? Ө, в2. Water 0° 45° 90° (a) (6)arrow_forwardWhen the sun is either rising or setting and appears to be just on the horizon, it is in fact below the horizon. The explanation for this seeming paradox is that light from the sun bends slightly when entering the earth’s atmosphere, as shown in Fig. Since our perception is based on the idea that light travels in straight lines, we perceive the light to be coming from an apparent position that is an angle d above the sun’s true position. (a) Make the simplifying assumptions that the atmosphere has uniform density, and hence uniform index of refraction n, and extends to a height h above the earth’s surface, at which point it abruptly stops. Show that the angle d is given by as attached. where R = 6378 km is the radius of the earth. (b) Calculate d using n = 1.0003 and h = 20 km. How does this compare to the angular radius of the sun, which is about one quarter of a degree? (In actuality a light ray from the sun bends gradually, not abruptly, since the density and refractive index of the…arrow_forwardWhich statement best describes the conditions necessary for humans to see objects? O A person can see an object when the object is in the line of the person's sight O A person can see an object whenever light shines on it O A person can see when light travels into his/her eyes and then to the object O A person can see an object when light waves that are emitted or reflected by the object enter the eyearrow_forward
- • During a daytime football game you notice that a player’s reflective helmet forms an image of the Sun 4.8 cm behind the surface ofthe helmet. What is the radius of curvature of the helmet, assuming it to be roughly spherical?arrow_forwardDistances in space are often quoted in units of light years, the distance light travels in one year (365.25 days). How many meters is a light year? Provide the solution: x 1015 marrow_forward•4 In Fig. 35-32a, a beam of light in material 1 is incident on a boundary at an angle of 30°. The extent to which the light is ben due to refraction depends, in part, on the index of refraction n, o material 2. Figure 35-32b gives the angle of refraction Oz versus n for a range of possible n2 values, from n, = 1.30 to n, = 1.90. Wha is the speed of light in material 1? в, 40° 300! 30° в, 20° по (a) (b)arrow_forward
- Two vectors are given as follows -3i + 6j – 5k and B = -2i + 3j + k. What is the %3D |3D difference between these two vectors? O-5i + 9j - 4k -6i + 18j - 5k O-i+ 3j - 6k -3i + 3j -6karrow_forward43-44. If a ray of light from a material with n = 1.2 points at an angle of incidence of 25° would have an angle of refraction of 40° from a second material, find the index of refraction of the second material. n= 0.74 n= 0.79 •n= 1.44 • n= 0.75arrow_forwardWhen a man stands near the edge of an empty drainage ditch of depth 2.80 m, he can barely see the boundary between the opposite wall and bottom of the ditch as in Figure (a) shown below. The distance from his eyes to the ground is h = 1.88 m. (Assume 0 = 27.6⁰.) a b ← ←P-| Ө m 2.80 m (a) What is the horizontal distance d from the man to the edge of the drainage ditch? d (b) After the drainage ditch is filled with water as in Figure (b) shown above, what is the maximum distance x the man can stand from the edge and still see the same boundary? X = marrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax