Lens Formula MCQs Quiz | Class 10
This quiz covers Class X Science (Code 086), Unit III: Natural Phenomena, focusing on the application of the Lens Formula. Test your understanding of how to use the lens formula to determine image position, nature, and magnification. After attempting all 10 multiple-choice questions, submit your answers to see your score and review correct solutions. You can also download a personalized PDF answer sheet for future reference.
Lens Formula: Application and Key Concepts
The lens formula is a fundamental relationship that describes how the focal length of a spherical lens relates to the object distance and image distance. Understanding this formula and its applications is crucial for analyzing the behavior of light as it passes through lenses.
The Lens Formula
The lens formula is given by:
1/v – 1/u = 1/f
Where:
- v is the image distance (distance of the image from the optical center of the lens).
- u is the object distance (distance of the object from the optical center of the lens).
- f is the focal length of the lens.
Magnification Formula
Magnification (m) describes how much larger or smaller an image is compared to the object. It is given by:
m = height of image (hi) / height of object (ho)
Also, for lenses:
m = v / u
New Cartesian Sign Convention
To consistently apply the lens formula, we use the New Cartesian Sign Convention:
- The optical center of the lens is taken as the origin (0,0).
- The principal axis is taken as the x-axis.
- All distances are measured from the optical center.
- Distances measured in the direction of incident light are taken as positive (+ve).
- Distances measured in the opposite direction of incident light are taken as negative (-ve).
- Distances measured perpendicular to and above the principal axis are positive (+ve).
- Distances measured perpendicular to and below the principal axis are negative (-ve).
Sign Conventions Summary for Lenses
| Quantity | Convex Lens | Concave Lens |
|---|---|---|
| Focal Length (f) | Positive | Negative |
| Object Distance (u) | Always Negative | Always Negative |
| Real Image (v) | Positive | Not applicable |
| Virtual Image (v) | Negative | Negative |
| Height of Object (ho) | Always Positive | Always Positive |
| Height of Real Image (hi) | Negative (inverted) | Not applicable |
| Height of Virtual Image (hi) | Positive (erect) | Positive (erect) |
Interpreting Magnification (m)
- If m is positive, the image is virtual and erect.
- If m is negative, the image is real and inverted.
- If |m| > 1, the image is magnified.
- If |m| < 1, the image is diminished.
- If |m| = 1, the image is of the same size as the object.
Applications of Lenses
Lenses have numerous applications in daily life and technology:
- Eyeglasses: Correcting vision defects like myopia (nearsightedness) using concave lenses and hypermetropia (farsightedness) using convex lenses.
- Cameras: Convex lenses focus light onto the film or sensor to capture images.
- Microscopes: A combination of convex lenses to produce highly magnified images of tiny objects.
- Telescopes: Used to view distant objects, employing convex lenses (refracting telescopes) or mirrors (reflecting telescopes).
- Projectors: Convex lenses are used to project magnified images onto a screen.
Quick Revision
- Lens Formula: 1/v – 1/u = 1/f
- Magnification: m = hi/ho = v/u
- Convex Lens: Converging lens, usually forms real images, positive focal length.
- Concave Lens: Diverging lens, always forms virtual, erect, and diminished images, negative focal length.
- Sign Conventions: Crucial for correct application of formulas.
Practice Questions (for self-study)
- An object is placed 60 cm from a convex lens of focal length 20 cm. Where is the image formed?
- A concave lens produces an image 10 cm from the lens for an object placed 20 cm from it. What is the focal length of the concave lens?
- If a convex lens forms an image at 30 cm from the lens when an object is placed 15 cm away, what is the magnification?
- An object 5 cm high is placed at 25 cm from a converging lens of focal length 10 cm. Find the height of the image.
- What type of lens is used to correct hypermetropia and why?
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