Question

In: Physics

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at...

Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in the figure .
their point of intersection, as shown in the figure .
yg.23.50.jpg
For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror(which is 28.0 cm long) after reflecting from the first mirror?


Solutions

Expert Solution

Concepts and reason

The concepts needed to solve this problem are the law of reflection, trigonometry ratio of tangent and the concept of alternative angles.

First, draw a needful ray diagram of the situation. Use the concept of alternative angle and the formula for trigonometry ratio of tangent and solve for required angle using the law of reflection.

Fundamentals

The formula for trigonometry ratio of tangent is,

tanθ=oppositesideoftheangleadjacentsideoftheangle{\rm{tan}}\theta = \frac{{{\rm{opposite side of the angle}}}}{{{\rm{adjacent side of the angle}}}}

Here, θ\theta is the angle.

One of the laws of reflection is that the angle of incidence is equal to the angle of reflection.

The needful ray diagram of the situation is as follows:

In the diagram, i1{i_1} is the incident angle at first incident, rr is angle of refraction at first incident, and i2{i_2} is the glancing angle of incident of light at midpoint of second mirror.

The formula for trigonometry ratio of tangent is,

tanθ=oppositesideoftheangleadjacentsideoftheangle{\rm{tan}}\theta = \frac{{{\rm{opposite side of the angle}}}}{{{\rm{adjacent side of the angle}}}}

Substitute i2{i_2} for θ\theta , 11.5 cm for opposite side of angle, and 14.0 cm for adjacent side of the angle.

tani2=11.5cm14.0cm=39.4\begin{array}{c}\\\tan {i_2} = \frac{{11.5{\rm{ cm}}}}{{14.0{\rm{ cm}}}}\\\\ = {\rm{39}}{\rm{.4}}^\circ \\\end{array}

In the diagram, the angle i2{i_2} and the angle r are alternative angles.

i2=r=39.4{i_2} = r = 39.4^\circ

From the law of reflection, the angle of incidence is equal to the angle of reflection.

i1=r=39.4{i_1} = r = 39.4^\circ

Ans:

The required value of angle of incidence is 39.439.4^\circ


Related Solutions

1. Three plane mirrors intersect at right angles. A beam of laser light strikes the first...
1. Three plane mirrors intersect at right angles. A beam of laser light strikes the first of them at an angle ? with respect to the normal a)Show that when this ray is reflected off of the other two mirrors and crosses the original ray, the angle ? between these two rays will be ?=180?? 2?. b)For what angle ? will the two rays be perpendicular when they cross? 2.A ray of light in diamond (index of refraction 2.42) is...
A wire bent with two right angles (forming a u-shape) sits in the xy-plane. The closed end (where the right angles are) is on the x-axis.
A wire bent with two right angles (forming a u-shape) sits in the xy-plane. The closed end (where the right angles are) is on the x-axis. The sides parallel to the y-axis run in the -y direction. A movable wire, parallel to the x-axis but not on the x-axis at any time, moves in the +y direction. If a magnetic field going in the -z direction baths the circuit, what is the direction of the induced current in the movable...
Show that if the opposite angles of a quadrilateral add up to two right angles, then...
Show that if the opposite angles of a quadrilateral add up to two right angles, then the vertices are concyclic
A 650-nm continuous-wave laser beam strikes a photodetector. The photon arrival rate is 4x10^16 photons per...
A 650-nm continuous-wave laser beam strikes a photodetector. The photon arrival rate is 4x10^16 photons per second, resulting in 6x10^16 electrons per second being collected at the photodetector's positive contact (i.e.,anode). 1. What is the average received optical power in mW? 2. What is the average photocurrent in the external circuit? 3. What is the quantum efficiency of the photodetector? 4. What is the responsivity? 5. Does this photodetector exhibit photocurrent gain?
For a Michelson interferometer, the distances of the two perpendicular mirrors from the beam splitter differ...
For a Michelson interferometer, the distances of the two perpendicular mirrors from the beam splitter differ by 1.7 mm. If the interferometer is equipped by a sodium source having n = 589 nm, (a) what is the order of the central spot? (b) Is the central spot dark or bright? (c) For the 1.7-mm separation between the two mirrors, find the angle of inclination of the observed third bright fringe relative to the optical axis. (d) This interferometer is used...
When two plane mirrors are parallel, such as on opposite walls in a barber shop, multiple...
When two plane mirrors are parallel, such as on opposite walls in a barber shop, multiple images arise because each image in one mirror serves as an object for the other mirror. An object is placed between parallel mirrors separated by 25 cm. The object is 15 cm in front of the left mirror and 10 cm in front of the right mirror. (a) Find the distance from the left mirror to the first four images in that mirror. __cm...
A person walks into a room that has, on opposite walls, two plane mirrors producing multiple...
A person walks into a room that has, on opposite walls, two plane mirrors producing multiple images. Find the distances from the person to the first three images seen in the left-hand mirror, when the person is 9.00 ft from the mirror on the left wall and 10.0 ft from the mirror on the right wall. first image ft second image ft third image ft
Two billiard balls of equal mass move at right angles and meet at the origin of...
Two billiard balls of equal mass move at right angles and meet at the origin of an xy coordinate system. Ball A is moving upward along the y axis at vA = 1.9m/s , and ball B is moving to the right along the x axis with speed vB = 5.4m/s . After the collision, assumed elastic, ball B is moving along the positive y axis(Figure 1) . What is the final direction of ball A? What are their two...
Experiment-I (Permanent Magnetic): Draw two lines at right angles to each other on the sheet of...
Experiment-I (Permanent Magnetic): Draw two lines at right angles to each other on the sheet of paper, then position the compass on it so that the pivot of the compass needle lies directly above the point of intersection of the lines. Turn the sheet of paper until the compass needle lies along the shorter line and mark the ends of this line N and S (see Fig. 4). Place the bar magnet on the sheet of paper at about 10...
Collimated atomic beam, saturated absorption and two-photon spectroscopy are three methods of Doppler-free laser spectroscopy. (i)...
Collimated atomic beam, saturated absorption and two-photon spectroscopy are three methods of Doppler-free laser spectroscopy. (i) In each case summarize briefly the principle of how the Doppler width is reduced or eliminated , (ii) Which method (methods) collects (collect) signal from all atoms illuminated by laser beams? (iii) In collimated beam spectroscopy the probe laser beam with the wavelength of 0.5 μm intersects the atomic beam (velocity of 300 m/s) at the angle of 70o (the angle between the wave...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT