two thin convex lenses of focal length 20cm and 40cm are in contact with each other. calculate the focal length and the power of the equivalent lens.?
Answers
Answer :-
• Equivalent focal length = 13.33 cm
• Equivalent power = + 7.5 D
Explanation :-
We have :-
→ Two convex lenses in contact .
→ Focal length of 1st lens (f₁) = 20 cm
→ Focal length of 2nd lens (f₂) = 40 cm
______________________________
Firstly, we have to calculate the equivalent focal length of the lens. For two lenses in contact, we have equivalent focal length as :-
1/f = 1/f₁ + 1/f₂
⇒ 1/f = 1/20 + 1/40
⇒ 1/f = (2 + 1)/40
⇒ 1/f = 3/40
⇒ 3f = 40
⇒ f = 40/3
⇒ f = 13.33 cm
Now, when focal length is in cm, then by using relationship between focal length and power of a lens, we get :-
P = 100/f
⇒ P = 100/13.33
⇒ P = 10000/13333
⇒ P = + 7.5 D
Answer:
◓ Equivalent focal length = 13.33 cm or 0.1333 m
◓ Equivalent power = + 7.5 D
Explanation:
Given information,
Two thin convex lenses of focal length 20 cm and 40 cm are in contact with each other. Calculate the equivalent focal length and the equivalent power of the lens?
Here,
◓ Focal length of 1st lens (f_{1}) = 20cm
◓ Focal length of 2nd lens (f_{2}) = 40cm
◓ Equivalent focal length = ?
◓ Equivalent power = ?
Firstly let's calculate the equivalent focal length. We clearly know that it is given by;
- 1/f = 1/f_{1} + 1/f_{2}
Putting all values,
➻ 1/f = 1/20 + 1/40
➻ 1/f = (1 × 2)/(20 × 2) + 1/40
➻ 1/f = 2/40 + 1/40
➻ 1/f = (2 + 1)/40
➻ 1/f = 3/40
By cross multiplication,
➻ 1 × 40 = 3 × f
➻ 40 = 3f
➻ 40/3 = f
➻ 13.33 = f
➻ f = 13.33 cm
Converting it into meters,
- 1m = 100cm
➻ f = 13.33/100
➻ f = 0.1333 m
- Hence, equivalent focal length is 0.1333 m.
Now, let's calculate the equivalent power. We clearly know that it is given by;
- P = 1/f
Putting all values,
➻ P = 1/0.1333
➻ P = (1 × 10000)/1333
➻ P = + 7.5 D
- Hence, equivalent power is + 7.5 D.
Learn more,
Related question:
- An object 2 cm height is placed 20 cm in front of convex lens of focal length 10cm.Find a distance from the lens at which a screen should be placed in order to obtained a sharp image. What will be size and nature of image formed.
Answer:
- brainly.in/question/44646702