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Converging and diverging lenses, thin lens equation, magnification, optical instruments
Learn step-by-step with practice exercises built right in.
Both sides of lens have same focal length!
A converging lens with focal length 15 cm is used to form an image of an object 30 cm away. Find (a) image distance, (b) magnification, (c) describe image.
Given:
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where:
Magnification:
๐ก Same equations as mirrors! But sign conventions differ slightly.
| Quantity | Positive | Negative |
|---|---|---|
| Converging | Diverging | |
| Real object | (rare) | |
| Real (opposite side) | Virtual (same side as object) | |
| Upright | Inverted |
Key difference from mirrors: Real image on opposite side of lens from object!
Draw any 2 of these 3 rays:
Where rays intersect = image location!
Cases:
where:
(Not commonly used in AP Physics 2, but good to know!)
Unit: Diopter (D) = mโปยน
Higher power โ shorter f โ more bending
Example: Eyeglass prescription "+2.00 D" means f = 0.50 m
Two lenses in combination:
Method 1 (Total power):
Method 2 (Step-by-step):
Nearsighted (myopia): Eyeball too long โ use diverging lens Farsighted (hyperopia): Eyeball too short โ use converging lens
Spherical aberration: Rays at edge focus differently
Chromatic aberration: Different colors focus at different points
โ Confusing lens and mirror sign conventions (real image location!) โ Forgetting f is negative for diverging lens โ Using wrong magnification formula for instruments โ Thinking diverging lens can form real image (never!) โ Not checking calculator mode (degrees vs radians)
Part (a): Image distance
Thin lens equation:
Part (b): Magnification
Part (c): Image description
Answer:
A diverging lens has focal length -20 cm. An object is placed 40 cm from the lens. Find the image distance and magnification.
Given:
Solution:
Thin lens equation:
Magnification:
Image description:
Answer:
Note: Diverging lenses ALWAYS produce virtual, upright, reduced images!
A converging lens with f = 10 cm is used as a magnifying glass. An object is placed 6 cm from the lens. Find the magnification.
Given:
Note: Object is inside focal length () - magnifying glass configuration!
Solution:
Find image distance:
Magnification:
Image description:
Answer: m = +2.5 (virtual, upright, enlarged)
This is why magnifying glasses work - object inside f gives enlarged virtual image!