Answer :
Sure, let's tackle each part of the problem step by step.
### Question 8:
Given:
- Time for the laser beam to travel to the Moon and back: \( t = 2.60 \ \text{seconds} \)
- Distance between Earth and the Moon: \( d = 3.85 \times 10^8 \ \text{meters} \)
To Find:
- Speed of light, \( c \)
Step-by-step solution:
1. Understanding the total distance traveled by the laser beam:
The laser beam travels from Earth to the Moon and back. Therefore, the total distance covered by the laser beam is twice the distance between Earth and the Moon.
[tex]\[ \text{Total Distance} = 2d = 2 \times 3.85 \times 10^8 \ \text{meters} \][/tex]
2. Calculate the total distance:
[tex]\[ 2 \times 3.85 \times 10^8 = 7.70 \times 10^8 \ \text{meters} \][/tex]
3. Using the formula for speed:
[tex]\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]
We want to calculate the speed of light, \( c \):
[tex]\[ c = \frac{7.70 \times 10^8 \ \text{meters}}{2.60 \ \text{seconds}} \][/tex]
4. Perform the division:
[tex]\[ c = \frac{7.70 \times 10^8}{2.60} \approx 2.96 \times 10^8 \ \text{meters/second} \][/tex]
Result:
The speed of light is approximately \( 2.96 \times 10^8 \ \text{meters/second} \).
### Question 9:
Understanding Diffraction and Wave Properties of Light:
1. Introduction to Diffraction:
Diffraction refers to the bending and spreading of waves when they pass through a narrow aperture or around an obstacle. This phenomenon is evidence of the wave nature of light.
2. Observation of Wave Behavior:
When light passes through a small slit, it doesn't continue in a straight line but instead spreads out in a pattern of light and dark bands called interference patterns. This pattern can only be explained if light behaves as a wave.
3. Conclusion:
The spreading out and creating of interference patterns by light waves when encountering obstacles or slits demonstrates that light exhibits wave-like properties, as these effects are characteristic features of wave behavior.
These principles, elaborated on pages 447-455, provide compelling evidence that light behaves like a wave through the phenomena of diffraction and interference.
### Question 8:
Given:
- Time for the laser beam to travel to the Moon and back: \( t = 2.60 \ \text{seconds} \)
- Distance between Earth and the Moon: \( d = 3.85 \times 10^8 \ \text{meters} \)
To Find:
- Speed of light, \( c \)
Step-by-step solution:
1. Understanding the total distance traveled by the laser beam:
The laser beam travels from Earth to the Moon and back. Therefore, the total distance covered by the laser beam is twice the distance between Earth and the Moon.
[tex]\[ \text{Total Distance} = 2d = 2 \times 3.85 \times 10^8 \ \text{meters} \][/tex]
2. Calculate the total distance:
[tex]\[ 2 \times 3.85 \times 10^8 = 7.70 \times 10^8 \ \text{meters} \][/tex]
3. Using the formula for speed:
[tex]\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \][/tex]
We want to calculate the speed of light, \( c \):
[tex]\[ c = \frac{7.70 \times 10^8 \ \text{meters}}{2.60 \ \text{seconds}} \][/tex]
4. Perform the division:
[tex]\[ c = \frac{7.70 \times 10^8}{2.60} \approx 2.96 \times 10^8 \ \text{meters/second} \][/tex]
Result:
The speed of light is approximately \( 2.96 \times 10^8 \ \text{meters/second} \).
### Question 9:
Understanding Diffraction and Wave Properties of Light:
1. Introduction to Diffraction:
Diffraction refers to the bending and spreading of waves when they pass through a narrow aperture or around an obstacle. This phenomenon is evidence of the wave nature of light.
2. Observation of Wave Behavior:
When light passes through a small slit, it doesn't continue in a straight line but instead spreads out in a pattern of light and dark bands called interference patterns. This pattern can only be explained if light behaves as a wave.
3. Conclusion:
The spreading out and creating of interference patterns by light waves when encountering obstacles or slits demonstrates that light exhibits wave-like properties, as these effects are characteristic features of wave behavior.
These principles, elaborated on pages 447-455, provide compelling evidence that light behaves like a wave through the phenomena of diffraction and interference.
