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A convex lens of focal length 20 em produces a real image twice the size of the object. Then the distance ofthe object from the lens is
- a)20 cm
- b)40 cm
- c)30 cm
- d)60 cm
Correct answer is option 'C'. Can you explain this answer?
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A convex lens of focal length 20 em produces a real image twice the si...
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A convex lens of focal length 20 em produces a real image twice the si...
Given:
- Focal length of the convex lens, f = 20 cm
- The real image produced by the lens is twice the size of the object.
To find:
The distance of the object from the lens.
Solution:
We can use the lens formula to solve this problem. The lens formula is given by:
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)
- u is the object distance from the lens (positive for real objects)
Step 1: Find the magnification of the lens.
The magnification (m) is given by the formula:
m = -v/u
Given that the image produced is twice the size of the object, we have:
m = -2
Step 2: Substitute the value of magnification in the lens formula.
We can rewrite the lens formula as:
1/f = 1/v + m/u
Substituting the given values:
1/20 = 1/v + (-2)/u
Simplifying the equation:
1/v = 1/20 + 2/u
1/v = (u + 40)/20u
Step 3: Substitute the value of v in terms of u into the lens formula.
Since the image distance v is twice the object distance u, we have:
v = 2u
Substituting this value in the lens formula:
1/(2u) = (u + 40)/20u
Simplifying the equation:
20u = 2(2u + 40)
20u = 4u + 80
16u = 80
u = 5 cm
Step 4: Convert the object distance from cm to em.
Since the given focal length is in em, we need to convert the object distance to em. 1 cm = 0.1 em, so:
u = 5 cm * 0.1 em/cm
u = 0.5 em
Therefore, the distance of the object from the lens is 0.5 em or 30 cm.
Hence, the correct answer is option 'C' (30 cm).
- Focal length of the convex lens, f = 20 cm
- The real image produced by the lens is twice the size of the object.
To find:
The distance of the object from the lens.
Solution:
We can use the lens formula to solve this problem. The lens formula is given by:
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)
- u is the object distance from the lens (positive for real objects)
Step 1: Find the magnification of the lens.
The magnification (m) is given by the formula:
m = -v/u
Given that the image produced is twice the size of the object, we have:
m = -2
Step 2: Substitute the value of magnification in the lens formula.
We can rewrite the lens formula as:
1/f = 1/v + m/u
Substituting the given values:
1/20 = 1/v + (-2)/u
Simplifying the equation:
1/v = 1/20 + 2/u
1/v = (u + 40)/20u
Step 3: Substitute the value of v in terms of u into the lens formula.
Since the image distance v is twice the object distance u, we have:
v = 2u
Substituting this value in the lens formula:
1/(2u) = (u + 40)/20u
Simplifying the equation:
20u = 2(2u + 40)
20u = 4u + 80
16u = 80
u = 5 cm
Step 4: Convert the object distance from cm to em.
Since the given focal length is in em, we need to convert the object distance to em. 1 cm = 0.1 em, so:
u = 5 cm * 0.1 em/cm
u = 0.5 em
Therefore, the distance of the object from the lens is 0.5 em or 30 cm.
Hence, the correct answer is option 'C' (30 cm).
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