A converging beam of light passes through a diverging lens of focal length 20cm and comes to focus at a distance 30cm behind the lens.Find the position at which beam would converge in the absence of lens?
Dont knw
To find the position at which the beam would converge in the absence of the lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- v is the image distance behind the lens (given as 30 cm)
- u is the object distance from the lens (which we want to find)
In the absence of the lens, the beam would converge at the focus (since the lens is diverging, it spreads out the beam). So, by substituting the given values into the lens formula, we can solve for u:
1/20cm = 1/30cm - 1/u
To simplify this equation, we need to find the common denominator:
1/20cm = (3 - 1/u) / 30cm
Now, cross multiplying:
30cm * 1/20cm = 3 - 1/u
Simplifying the equation:
1.5 = 3 - 1/u
Rearranging the equation to solve for u:
1/u = 3 - 1.5
1/u = 1.5
Now, taking the reciprocal of both sides:
u = 1/1.5
u = 0.67 m
Therefore, in the absence of the lens, the beam would converge at a distance of 0.67 meters (or 67 centimeters) in front of the lens.