2 lenses in contact of power 3D and -5D form a composite lens. An object is placed around a distance 50 cm from this composite lens,find the position of the image.
The power of the lens combination
=P1+P2=3-5=-2D
The focal length of lens=1/p
= -100/2=-50 cm
We know the lens formula,1/f=1/v-1/u
now u=-50 cm
-1/50=1/v+1/150
Now solve it....
After you will get -25 as v.
Therefore,position of image is 25 cm from the composite lens.
Here
F= 1/p =1/-2
But u have gave it as 100/2
How it is possible?
To find the position of the image formed by the composite lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
Let's first calculate the effective focal length (F) of the composite lens:
F = f1 + f2
where:
f1 = focal length of the first lens (3D)
f2 = focal length of the second lens (-5D)
Since the focal length is given in diopters (D), which is the inverse of meters, we can convert it to meters by taking the reciprocal (1/f):
f1 = 1/3 = 0.33 meters
f2 = -1/5 = -0.20 meters
F = 0.33 + (-0.20) = 0.13 meters
Now, let's calculate the object distance (u) from the composite lens. Since the object is placed 50 cm from the lens, convert it to meters:
u = 50 cm = 0.50 meters
Using the lens formula, we can solve for the image distance (v):
1/F = 1/v - 1/u
1/0.13 = 1/v - 1/0.50
7.69 = 1/v - 2
1/v = 7.69 + 2
1/v = 9.69
v = 1/9.69
v ≈ 0.10 meters
Therefore, the position of the image formed by the composite lens is approximately 0.10 meters from the lens in front of it.
To find the position of the image formed by the composite lens, you can use the lens makers formula and the concept of refraction of light through thin lenses.
Step 1: Determine the focal lengths of the individual lenses.
The power of a lens is given by the formula P = 1/f, where P is the power of the lens in diopters (D) and f is the focal length of the lens in meters (m).
For the lens with a power of +3D, the focal length (f1) can be calculated as 1/3 = 0.33 m or 33 cm.
For the lens with a power of -5D, the focal length (f2) can be calculated as 1/-5 = -0.2 m or -20 cm.
Step 2: Calculate the equivalent focal length of the composite lens.
The formula for calculating the equivalent focal length (F) of two lenses in contact is given by the formula:
1/F = 1/f1 + 1/f2.
Substituting the values, we get:
1/F = 1/33 + 1/-20.
Solving this equation gives us the value of F, which is the equivalent focal length of the composite lens.
Step 3: Determine the position of the image using the lens formula.
The lens formula is given by:
1/v - 1/u = 1/f,
where v is the distance of the image from the lens, u is the distance of the object from the lens, and f is the focal length of the lens.
Given: u = -50 cm (since the object is placed 50 cm from the lens).
Now, substitute the calculated value of F and the given value of u into the lens formula to solve for v:
1/v - 1/(-50) = 1/F.
Solve for v to find the position of the image formed by the composite lens.
Please note that in this case, since the object is placed on the same side as the lens with negative focal length, the image formed will be virtual and upright.