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A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.
- a)0.32 nm
- b)0.2 nm
- c)0.3 nm
- d)0.25 nm
Correct answer is option 'B'. Can you explain this answer?
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A parallel beam of light of wavelength 500 nm falls on a narrow slit a...
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A parallel beam of light of wavelength 500 nm falls on a narrow slit a...
Given:
- Wavelength of light, λ = 500 nm = 500 × 10^-9 m
- Distance between the screen and the slit, L = 1 m
- Distance of the first minimum from the center of the screen, x = 2.5 mm = 2.5 × 10^-3 m
To find:
- Width of the slit, a
Formula used:
The distance of the nth minimum from the center of the screen is given by the formula:
x = (nλL) / a
Calculation:
- Rearranging the formula, we have:
a = (nλL) / x
- Substituting the given values, we have:
a = (1 × 500 × 10^-9 × 1) / (2.5 × 10^-3)
a = 200 × 10^-9 / 2.5 × 10^-3
a = 80 × 10^-6 / 1 × 10^-3
a = 80 × 10^-6 × 10^3
a = 80 × 10^-6 × 10^3
a = 80 × 10^-3
a = 0.08 mm
- Converting the width of the slit from millimeters to nanometers:
a = 0.08 mm = 0.08 × 10^-3 m = 80 × 10^-6 m = 80 nm
Therefore, the width of the slit is 0.08 mm or 80 nm, which is approximately equal to option B.
- Wavelength of light, λ = 500 nm = 500 × 10^-9 m
- Distance between the screen and the slit, L = 1 m
- Distance of the first minimum from the center of the screen, x = 2.5 mm = 2.5 × 10^-3 m
To find:
- Width of the slit, a
Formula used:
The distance of the nth minimum from the center of the screen is given by the formula:
x = (nλL) / a
Calculation:
- Rearranging the formula, we have:
a = (nλL) / x
- Substituting the given values, we have:
a = (1 × 500 × 10^-9 × 1) / (2.5 × 10^-3)
a = 200 × 10^-9 / 2.5 × 10^-3
a = 80 × 10^-6 / 1 × 10^-3
a = 80 × 10^-6 × 10^3
a = 80 × 10^-6 × 10^3
a = 80 × 10^-3
a = 0.08 mm
- Converting the width of the slit from millimeters to nanometers:
a = 0.08 mm = 0.08 × 10^-3 m = 80 × 10^-6 m = 80 nm
Therefore, the width of the slit is 0.08 mm or 80 nm, which is approximately equal to option B.
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A parallel beam of light of wavelength 500 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 1 m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Find the width of the slit.a)0.32 nmb)0.2 nmc)0.3 nmd)0.25 nmCorrect answer is option 'B'. Can you explain this answer?
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