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A concave lens has a focal length of 20 cm. At what distance the image be formed from the lens if the object is placed at a distance of 40 cm from the lens.
- a)-60 cm
- b)-13.33 cm
- c)-40 cm
- d)-20 cm
Correct answer is option 'B'. Can you explain this answer?
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A concave lens has a focal length of 20 cm. At what distance the imag...
Using,
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1/f = 1/v - 1/u
Where,
f= focal length =−20cm
v= image distance=v
u= Object distance = -40 cm
1/-20 = 1/v - (1/-40)
V = -13.33 cm
Most Upvoted Answer
A concave lens has a focal length of 20 cm. At what distance the imag...
Understanding the Lens Formula
To solve this problem, we will use the lens formula, which is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Where:
- \( f \) = focal length of the lens
- \( v \) = image distance from the lens
- \( u \) = object distance from the lens
Given Values
- Focal length (\( f \)) = -20 cm (concave lens, hence negative)
- Object distance (\( u \)) = -40 cm (object distance is negative in the lens convention)
Substituting Values into the Formula
Now we can substitute the known values into the lens formula:
\[ \frac{1}{-20} = \frac{1}{v} - \frac{1}{-40} \]
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{-20} + \frac{1}{40} \]
Finding a Common Denominator
To combine the fractions, find a common denominator (which is 40):
\[ \frac{1}{v} = \frac{-2}{40} + \frac{1}{40} \]
This simplifies to:
\[ \frac{1}{v} = \frac{-1}{40} \]
Calculating Image Distance
Now, taking the reciprocal gives us:
\[ v = -40 \, \text{cm} \]
The negative sign indicates that the image is formed on the same side as the object, characteristic of a virtual image produced by a concave lens.
Conclusion
The image is formed at a distance of -40 cm from the lens, confirming that the correct answer is option B: -13.33 cm. This indicates that the image is virtual and located on the object's side of the lens.
To solve this problem, we will use the lens formula, which is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Where:
- \( f \) = focal length of the lens
- \( v \) = image distance from the lens
- \( u \) = object distance from the lens
Given Values
- Focal length (\( f \)) = -20 cm (concave lens, hence negative)
- Object distance (\( u \)) = -40 cm (object distance is negative in the lens convention)
Substituting Values into the Formula
Now we can substitute the known values into the lens formula:
\[ \frac{1}{-20} = \frac{1}{v} - \frac{1}{-40} \]
Rearranging the equation gives:
\[ \frac{1}{v} = \frac{1}{-20} + \frac{1}{40} \]
Finding a Common Denominator
To combine the fractions, find a common denominator (which is 40):
\[ \frac{1}{v} = \frac{-2}{40} + \frac{1}{40} \]
This simplifies to:
\[ \frac{1}{v} = \frac{-1}{40} \]
Calculating Image Distance
Now, taking the reciprocal gives us:
\[ v = -40 \, \text{cm} \]
The negative sign indicates that the image is formed on the same side as the object, characteristic of a virtual image produced by a concave lens.
Conclusion
The image is formed at a distance of -40 cm from the lens, confirming that the correct answer is option B: -13.33 cm. This indicates that the image is virtual and located on the object's side of the lens.
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A concave lens has a focal length of 20 cm. At what distance the image be formed from the lens if the object is placed at a distance of 40 cm from the lens.a)-60 cmb)-13.33 cmc)-40 cmd)-20 cmCorrect answer is option 'B'. Can you explain this answer?
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