Show all your works in detail. Substitute numerical values where required. A fil

Question

Show all your works in detail. Substitute numerical values where required. A film of MgF_2 (n = 1.38) having thickness 1.00 times 10^-5 cm used camera lens. (a) What are the three longest wavelengths that are intensified in the reflected light? (b) Are any of these wavelengths in the visible Young's double-slit experiment is performed with 589-nm light and a distance of 2.00 m between the slits and the screen. The tenth interference minimum is observed 7.26 mm from the central maximum. Determine the spacing of the slits. A concave mirror forms an inverted image four times larger than the object. Find the focal length of the mirror, assuming the distance between object and image is 0.6 m. An unpolarized light 3 W/m^2 in intensity is passed through a polarizer and two other analyzers as depicted below. The transmission axes are theta_1 = 10 degree, theta_2 = 40 degree and theta_3 = 60 degree with respect to the vertical axis. What is the intensity of the light after it passes the last analyzer? Polarizer analyzer A concave mirror has a radius of curvature of 30.0 cm. Calculate the image position and magnification of an object placed in front of the mirror at distances of (a) 60 cm and (b) 15 cm. (c) Draw ray diagrams to obtain the image characteristics in each case. A converging lens has a focal length of 30.0 cm. find the image for object distances of (a) 60 cm, (b) 15 cm. and 10 cm. For each case, state whether the image is real or virtual and upright or inverted. Find the magnification in each case. A screen is placed 80.0 cm from a single slit, which is illuminated with 690-nm light. If the distance between the first and third minima in the diffraction pattern is 4.00 mm, what is the width of the slit? The hydrogen spectrum has a red line at 656 nm and a blue line at 434 nm. What are the angular separations between these two spectral lines obtained with a diffraction grating that 4200 groves/cm?

Explanation / Answer

path difference = 2*t

lambda in film = lambda in air/n

for intensidied in relfected light pateh diference = m*lambda in film

2t = m*lambda in air/n

lambda in air = 2tn/m

for m = 1

lambda in air = 2*10^-5*10^-2*1.38/1 = 276 nm

for m = 2

lambda in air = 2*10^-5*10^-2*1.38/2 = 138 nm

for m = 3

lambda in air = 2*10^-5*10^-2*1.38/3 = 92 nm

(b)NO

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2)

In double slit interference

y = m*lambda*R/d

y = 7.26 mm

m = 10

lambda = 589 nm

R = 2 m

7.26*10^-3 = 10*589*10^-9*2/d

d = 1.62 mm <<<<<-----answer

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3)

magnification m = s'/s = 4

s' = 4s

image distance = s'

object distance = s = 0.6 m

1/s + 1/s' = 1/f

1/0.6 + 1/(4*0.6) = 1/f

f = 0.48 m

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Intensity of light after passing through Ist polarizer I1 = I0/2

Intensity of light after passing through 2nd polarizer I2 = I1*(costheta2)^2

Intensity of light after passing through 2nd polarizer I3 = I2*(costheta3)^2

I3 = I1*(cos(theta2-theta1))^2*(cos(theta3-theta2))^2

I3 = Io*(cos(theta2-theta1))^2*(cos(theta3-theta2))^2

I3 = (3/2)*(cos(40-10))^2*(cos(60-40))^2

I3 = 0.994 W/m^2

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6)

object distance s = 60 cm

focal length f = 30 cm

image distance s' = ?

1/s + 1/s' = 1/f

1/60 + 1/s' = 1/30

s' = 60 cm

real

m = s'/s = 1

(b)

object distance s = 15 cm

focal length f = 30 cm

image distance s' = ?

1/s + 1/s' = 1/f

1/15 + 1/s' = 1/30

s' = -30 cm

virtual

m = -s'/s = 30/15 = 2

(c)

object distance s = 10 cm

focal length f = 30 cm

image distance s' = ?

1/s + 1/s' = 1/f

1/10 + 1/s' = 1/30

s' = -15 cm

virtual

m = -s'/s = 15/10 = 1.5

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