A convex lens from a real and inverted image of a needle at a distance of 50 cm from it . where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also find the power of the lens
Answers
Answer:
4 d power
Explanation:
In this solution we will use the lens formula 1v−1u=1f …… (i).
Here, v and u are the positions of the image and the object with respect to the lens, according to the sign convection. f is the focal length of the lens.
It is said that when the needle is placed in front of the lens, a real and inverted image is formed and the size of the image is equal to the size of the needle.
The magnification is defined as the ratio of the size of the image to the size of the object. The value of magnification is given as m=vu.
In this case, m= -1 because the image is inverted.
⇒−1=vu
⇒v=−u.
It is given that the image is formed at a distance of 50cm from the lens. And since the image is real, v = +50cm.
This means that u = -50cm.
Therefore, the needle must be placed at a distance of 50cm from the lens.
Substitute the values of v and u in (i).
⇒150−1−50=1f
⇒1f=250=125
⇒f=25cm.
Therefore, the focal length of the convex lens is 25cm.
Power of a lens is given as P=1f.
⇒P=125cm−1
⇒P=125(10−2m)−1=10025m−1=4m−1.
1m−1=1D
⇒P=4D
This means that power of the given lens is 4D (dioptre).
Answer:
Question
Answers
A convex lens forms a real and inverted image of a needle at a distance of 50cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also find the power of the lens.
Answer
VerifiedVerified
29.9K+ Views
6 Likes
Hint: It is given that the image of the needle is formed at a distance of 50cm from the lens and the image is real and inverted. In addition, the sizes of the image and the needle are equal. So use the magnification formula. Then use the lens formula and find the focal length. With the focal length calculate the power of the lens.
Formula used:
1v−1u=1f
m=vu
Complete answer:
In this solution we will use the lens formula 1v−1u=1f …… (i).
Here, v and u are the positions of the image and the object with respect to the lens, according to the sign convection. f is the focal length of the lens.
It is said that when the needle is placed in front of the lens, a real and inverted image is formed and the size of the image is equal to the size of the needle.
The magnification is defined as the ratio of the size of the image to the size of the object. The value of magnification is given as m=vu.
In this case, m= -1 because the image is inverted.
⇒−1=vu
⇒v=−u.
It is given that the image is formed at a distance of 50cm from the lens. And since the image is real, v = +50cm.
This means that u = -50cm.
Therefore, the needle must be placed at a distance of 50cm from the lens.
Substitute the values of v and u in (i).
⇒150−1−50=1f
⇒1f=250=125
⇒f=25cm.
Therefore, the focal length of the convex lens is 25cm.