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A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²?
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A cylindrical laser beam of diameter 4mm and power 10mW is incident on...
Solution:
Given:
Diameter of beam, d = 4mm
Power of the beam, P = 10mW
Focal length of convex lens, f = 10cm
Distance between lens and laser beam, u = 2m
Intensity at image will be calculated.
Step 1: Finding the radius of the beam
Radius of the beam, r = d/2 = 2mm
Step 2: Finding the area of the beam
Area of the beam, A = πr² = 3.14 x (2 x 10^-3)² = 12.56 x 10^-6 m²
Step 3: Finding the power per unit area
Power per unit area, I = P/A = (10 x 10^-3)/ (12.56 x 10^-6) = 795.77 W/m²
Step 4: Finding the image distance
Using the lens formula:
1/f = 1/u + 1/v
Where v is the image distance.
1/10 = 1/200 + 1/v
v = 9.9 cm
Step 5: Finding the image area
Using magnification formula:
magnification = (image height)/(object height) = v/u
As the object height is negligible compared to the image height, we can take magnification as:
magnification = v/u = 9.9/200 = 0.0495
Image area, A' = A/magnification² = 12.56 x 10^-6 / (0.0495)² = 5.59 x 10^-4 m²
Step 6: Finding the intensity at image
Intensity at image, I' = P/A' = (10 x 10^-3) / (5.59 x 10^-4) = 17.86 kW/m²
Answer:
The intensity at the image will be 17.86 kW/m², which is approximately equal to 18 MW/m². Therefore, option (5) is the correct answer.
Given:
Diameter of beam, d = 4mm
Power of the beam, P = 10mW
Focal length of convex lens, f = 10cm
Distance between lens and laser beam, u = 2m
Intensity at image will be calculated.
Step 1: Finding the radius of the beam
Radius of the beam, r = d/2 = 2mm
Step 2: Finding the area of the beam
Area of the beam, A = πr² = 3.14 x (2 x 10^-3)² = 12.56 x 10^-6 m²
Step 3: Finding the power per unit area
Power per unit area, I = P/A = (10 x 10^-3)/ (12.56 x 10^-6) = 795.77 W/m²
Step 4: Finding the image distance
Using the lens formula:
1/f = 1/u + 1/v
Where v is the image distance.
1/10 = 1/200 + 1/v
v = 9.9 cm
Step 5: Finding the image area
Using magnification formula:
magnification = (image height)/(object height) = v/u
As the object height is negligible compared to the image height, we can take magnification as:
magnification = v/u = 9.9/200 = 0.0495
Image area, A' = A/magnification² = 12.56 x 10^-6 / (0.0495)² = 5.59 x 10^-4 m²
Step 6: Finding the intensity at image
Intensity at image, I' = P/A' = (10 x 10^-3) / (5.59 x 10^-4) = 17.86 kW/m²
Answer:
The intensity at the image will be 17.86 kW/m², which is approximately equal to 18 MW/m². Therefore, option (5) is the correct answer.
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A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²?
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A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²?.
A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical laser beam of diameter 4mm and power 10mW is incident on a convex lens of focal length 10 cm kept 2m away. Intensity at image will be : (1) 0.29 MW/m² (3) 10 MW/m² (2) 7 MW/m² (4) 29 MW/m²?.
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