Value of theta of first minimum

In summary, the conversation discusses a problem with calculating the angle of incidence for a parallel beam of monochromatic light on a diffraction grating. The separation between successive lines on the grating is 0.7 μm and the wavelength of the light is 580 nm. The individual is confused about the given answer of 56° and their calculated answer of 47°, as they used the incorrect value of 70 μm for the separation between slits. The correct value is 0.7 μm.
  • #1
desmond iking
284
2

Homework Statement


A parallel beam of monochromatic light of wavelength 580nm is incidentally normal on a diffraction grating. The separation between successive lines on the grating is 0.7μm as shown in the figure.
please refer to the photo , i am having problem with part (a)


Homework Equations





The Attempt at a Solution


my working is d sin θ = λ
sin θ = λ /d , where d is the separation between slits.. by plug in value of λ = 580x10^-9 and d = 1/ (5000x10^2) , i have my θ = 47 ° , the ans given is 56°
why am i wrong?
 

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  • #2
Where are you given that value for d?
 
Last edited:
  • #3
NascentOxygen said:
Where are you given that value for d?

sorry i made a typo.
here's what i mean :
sin θ = λ /d , where d is the separation between slits.. by plug in value of λ = 580x10^-9 and d = 0.7x10^-6 , i have my θ = 47 ° , the ans given is 56°
 
  • #4
Part a asks about a single slit !
And the distance between slits is NOT 70 micrometer.
 
  • #5


I would like to provide an explanation for the discrepancy between your calculated value and the given answer. Firstly, it is important to note that the value of theta for the first minimum is dependent on the number of slits on the diffraction grating and the wavelength of the incident light. In this case, the given value of the separation between slits (0.7μm) seems to be incorrect, as it is very small compared to the wavelength of the incident light (580nm). This could be a typo or a mistake in the given information.

Assuming that the separation between slits is actually 0.7mm (as shown in the figure), your calculation is correct and the given answer of 56° is incorrect. This is because the smaller the slit separation, the wider the angle of diffraction for the first minimum. This can be seen by comparing your calculated value of 47° to the given answer of 56°. The smaller slit separation results in a larger angle of diffraction.

In conclusion, it is important to carefully check the given information and equations when solving problems in science. In this case, the incorrect value of the slit separation led to an incorrect answer. By using the correct value, your calculation is correct and the given answer is incorrect.
 

1. What is the value of theta of the first minimum?

The value of theta of the first minimum is the angle at which the first minimum occurs in a diffraction pattern. It is typically denoted as θ₁ and is dependent on the wavelength of the incident light, the distance between the slits or obstacles, and the size of the slit or obstacle.

2. How is the value of theta of the first minimum calculated?

The value of theta of the first minimum is calculated using the equation θ₁ = λ/d, where λ is the wavelength of the incident light and d is the distance between the slits or obstacles. This equation is based on the concept of diffraction and interference of light waves.

3. What is the significance of the value of theta of the first minimum?

The value of theta of the first minimum is significant because it represents the angle at which the first minimum occurs in a diffraction pattern. This angle can provide information about the properties of the diffracting material, such as the size of the slits or obstacles, and can also be used to calculate the wavelength of the incident light.

4. What factors can affect the value of theta of the first minimum?

The value of theta of the first minimum can be affected by various factors such as the wavelength of the incident light, the distance between the slits or obstacles, and the size of the slits or obstacles. Other factors that may influence this value include the properties of the diffracting material, the angle of incidence, and any external sources of interference.

5. How does the value of theta of the first minimum change with different conditions?

The value of theta of the first minimum can change with different conditions due to the factors mentioned above. For example, if the distance between the slits or obstacles is increased, the value of theta of the first minimum will also increase. Similarly, if the wavelength of the incident light is changed, the value of theta of the first minimum will also change accordingly. It is important to consider all relevant conditions when calculating or interpreting the value of theta of the first minimum.

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