Refractive index

The light passes through the interface between air and glass with a refractive index of 1.5. Find:
(a) the angle of refraction if light strikes the interface from the air at an angle of 40°.
(b) the angle of refraction when light strikes the glass interface at an angle of 40°.
(c) the angle of incidence if the light is refracted at an angle of 20° on impact from the glass.
(d) cut-off angle (justify for which way the light passes through the interface)

Correct answer:

A =  25.374 °
B =  74.6186 °
C =  30.8659 °
D =  41.8103 °

Step-by-step explanation:

n=1.5 α=40  sinα:sinA=n  A1=arcsin(sinα/n)=arcsin(sin40 /n)=arcsin(sin40 /1.5)=arcsin(0.642788/1.5)=0.44286 A=A1=A1 180π=0.4429 180π=25.374=252226"
β=40  sinB:sinβ=n  B1=arcsin(n sinβ)=arcsin(n sin40 )=arcsin(1.5 sin40 )=arcsin(1.5 0.642788)=1.30234 B=B1=B1 180π=1.3023 180π=74.619=74.6186=74377"
γ=20  sinC:sinγ=n  C1=arcsin(n sinγ)=arcsin(n sin20 )=arcsin(1.5 sin20 )=arcsin(1.5 0.34202)=0.53871 C=C1=C1 180π=0.5387 180π=30.866=30.8659=305157"
δ=90  sinδ:sinD=n  D1=arcsin(sinδ/n)=arcsin(sin90 /n)=arcsin(sin90 /1.5)=arcsin(1/1.5)=0.72973 D=D1=D1 180π=0.7297 180π=41.81=41.8103=414837"



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




Tips to related online calculators
Check out our ratio calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

Related math problems and questions:

  • Resultant force
    3forces Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
  • Hot air balloon
    balloon The center of the balloon is at an altitude of 600 m above the ground (AGL). From habitat on earth is the center of the balloon to see in elevation angle 38°20' and the balloon is seen from the perspective of angle 1°16'. Calculate the diameter of the bal
  • Building
    building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
  • Bearing
    compass A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
  • Scalar dot product
    dot_product Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
  • Elevation angles
    mountain From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
  • Two forces
    vector-add Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer.
  • Mast
    stoziar Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast, if the sun above the horizon is at angle 45°12'.
  • Quadrilateral oblique prism
    kosyHranol What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
  • Reflector
    lamp Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
  • Altitude angle
    balloon In complete winds-free weather, the balloon took off and remained standing exactly above the place from which it took off. It is 250 meters away from us. How high did the balloon fly when we see it at an altitude angle of 25°?
  • Sound speed in Earth
    speed Through the surface layers of the Earth, sound propagates 13 times faster than through air. During the geological survey, the charge exploded 1.7 km from the measuring station. How long does it take between the vibration of the soil at the measuring point
  • Calculate
    triangle_ssh Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
  • Aircraft
    aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
  • Aircraft
    aircraft-02 From the aircraft flying at an altitude of 500m, they observed places A and B (located at the same altitude) in the direction of flight at depth angles alpha = 48° and beta = 35°. What is the distance between places A and B?
  • Cable car
    lanovka Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
  • Powerplant chimney
    komin2 From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?