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guapka [62]
3 years ago
7

Unpolarized light with an intensity of 432 W/m^2 passes through three polarizing filters in a row, each of which is rotated 30 d

egrees from the one before it. Find the intensity of the light that emerges at the end
Physics
1 answer:
liraira [26]3 years ago
3 0

Answer:

40.5 W/m²

Explanation:

Intensity of unpolarized light = 432 W/m² = I₀

Intensity of light as it passes through first polarizer

I = I₀×0.5

⇒I = 432×0.5

⇒I = 216 W/m²

Intensity of light as it passes through second polarizer. So, Intensity after it passes through first polarizer is the input for the second polarizer

I = I₀×0.5 cos²30

⇒I = 216×0.75

⇒I = 162 W/m²

Intensity of light as it passes through third polarizer.

I = I₀×0.5 cos²30×cos²60

⇒I = 162×0.25

⇒I = 40.5 W/m²

Intensity of light at the end is 40.5 W/m²

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Length of longer pendulum = 99.3 cm

Length of shorter pendulum = 82.2 cm

Explanation:

Since the longer pendulum undergoes 10 oscillations in 20 s, its period T = 20 s/10 = 2 s.

From T = 2π√(l/g), the length of the pendulum. l = T²g/4π²

substituting T = 2s and g = 9.8 m/s² we have

l = T²g/4π²

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So, n₂ = n₁ + x. Also n₁ = t/T₁ and n₂ = t/T₂ where T₂ = period of shorter pendulum.

t/T₂ = t/T₁ + x

1/T₂ = 1/T₁ + x  (1)

Also, the T₂ = t/n₂ = t/(n₁ + x)  (2)

From (1) T₂ = T₁/(T₁ + x) (3)

equating (2) and (3) we have

t/(n₁ + x) = T₁/(T₁ + x)

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(10 + x) = 10(2 + x)

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collecting like terms

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9x = 10

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x = 1.11

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substituting x into (2)

T₂ = t/n₂ = t/(n₁ + x)

= 20/(10 + 1)

= 20/11

= 1.82 s

Since length l = T²g/4π²

substituting T = 1.82 s and g = 9.8 m/s² we have

l = T²g/4π²

= (1.82 s)² × 9.8 m/s² ÷ 4π²

= 32.46 m ÷ 4π²

= 0.822 m

= 82.2 cm

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