A concave lens or focal lens 10cm produce an erect image 40cm from the lens .Determine the object distance and magnification.
To determine the object distance and magnification, we can use the lens formula and the magnification formula.
The lens formula is given as:
1/f = 1/v - 1/u
where:
f is the focal length of the lens,
v is the image distance from the lens (positive for real images and negative for virtual images),
u is the object distance from the lens (positive for objects on the same side as the incident light and negative for objects on the opposite side).
Here, it is given that the lens is a concave lens with a focal length of 10 cm and that it produces an erect image 40 cm from the lens. We need to determine the object distance (u) and magnification (m).
Step 1: Determine the image distance (v):
Since it is given that the image is erect and 40 cm from the lens, we can say that the image distance (v) = +40 cm.
Step 2: Substitute the given values into the lens equation:
1/f = 1/v - 1/u
Substituting f = -10 cm and v = +40 cm into the equation, we get:
1/-10 = 1/40 - 1/u
Step 3: Solve for the object distance (u):
Rearranging the equation to solve for u, we have:
1/u = 1/40 - 1/-10
1/u = (1 - 4)/40
1/u = -3/40
u = -40/3 cm
Therefore, the object distance is u = -40/3 cm.
Step 4: Calculate magnification (m):
The magnification (m) is given by the formula:
m = -v/u
Substituting the values of u = -40/3 cm and v = +40 cm, we have:
m = -40 / (-40/3)
m = 3
Therefore, the magnification is m = 3.
In summary, the object distance is u = -40/3 cm and the magnification is m = 3.