Difference Between Convex and Concave Lenses with Examples and Images
Convex and Concave Lenses play a crucial role in optics, especially for JEE Main Physics learners. Understanding their structure, image formation, properties, and formulas is essential for mastering problems on lenses, magnification, and optical instruments. These lenses underpin fundamental concepts in refraction and are tested in almost every JEE optics section.
A convex lens is thicker at the center and converges parallel rays of light to a point. In contrast, a concave lens is thinner at the center and diverges incoming light rays. Both lenses follow the principles of refraction and require precise application of the lens formula and sign conventions.
Difference Between Convex and Concave Lenses
| Criteria | Convex Lens | Concave Lens |
|---|---|---|
| Shape | Thicker at centre; converging | Thinner at centre; diverging |
| Image Formation | Forms real or virtual images | Forms only virtual images |
| Applications | Magnifying glass, camera, microscope | Eyeglasses for myopia, peepholes |
| Focal Length Sign | Positive (+f) | Negative (−f) |
The main distinction in image formation is that a convex lens can form both real and virtual images depending on the object's position, while a concave lens always forms a virtual, upright, and diminished image.
Ray Diagrams and Image Formation by Convex and Concave Lenses
Drawing ray diagrams correctly is essential for JEE image-related questions. For a convex lens, three principal rays are common: a ray parallel to the principal axis (refracted through the focus), a ray passing through the optical center (undeviated), and a ray passing through the focus (emerges parallel).
For concave lenses, parallel rays diverge as if originating from the principal focus on the same side. Every diagram must respect the sign convention (left to right as positive) adopted in sign convention of lens and mirror for error-free numerical solutions.
In JEE, you may be asked to construct or interpret image location, size, and type based on object placement, especially relative to the lens's focal length (f) and radius of curvature (R).
Lens Formula, Sign Convention, and Magnification in Convex and Concave Lenses
Both convex and concave lenses obey the Thin Lens Formula:
- 1/v − 1/u = 1/f
Here, u is object distance, v is image distance, and f is focal length. For a convex lens, f is positive; for a concave lens, f is negative. Always use SI units and the Cartesian sign convention when solving problems.
Magnification (m) is given as:
- m = v/u
- Also, m = h'/h where h' is image height and h is object height.
A common JEE trap is neglecting the minus sign for concave lenses, which leads to wrong image nature or size. Review ray diagrams and sign usage in each calculation, referencing magnification for comparison.
Numerical Example Using Convex and Concave Lenses
A 2.0 cm tall object is placed 12 cm from a convex lens of focal length 6 cm. Find the image distance and nature.
- Given: u = -12 cm, f = +6 cm (convex lens), h = 2.0 cm
- Using 1/v − 1/u = 1/f:
- 1/v = 1/6 + 1/12 = (2+1)/12 = 3/12 = 1/4
- So, v = 4 cm (positive: real image on other side)
- Magnification m = v/u = 4/(-12) = -1/3 → Image is inverted, real, diminished.
- Final Answer: v = +4 cm; the image is real and inverted.
Convex and concave lens numericals often test application of formulae, units, and correct sign placement. For combined lenses, use the power addition principle as detailed in relevant combination of thin lenses topics.
Applications and Important Uses of Convex and Concave Lenses
- Convex lenses are used in microscopes, projectors, and cameras for image magnification.
- Concave lenses help correct myopia and are found in eyeglasses.
- Both types are integral to telescopes and various optical scientific devices.
- Convex lenses are used in magnifying glasses; concave lenses serve as peepholes in doors.
- Human eyes contain a natural convex lens system.
For deeper insight, the difference between lens and mirror is another frequent comparison in JEE optics. Always cross-link optical formulas and real-life contexts for optimal retention and speedy revision.
Common Mistakes and Best Practices for JEE: Convex and Concave Lenses
- Always apply the correct sign convention—objects left of the lens are taken as negative.
- For concave lenses, f is negative; for convex, f is positive.
- Draw ray diagrams stepwise using principal rays, especially for questions demanding image nature or position.
- Carefully read whether the problem asks for distance from lens, object, or focus.
Regular practice with authentic JEE Main problems, and cross-verifying steps with reliable resources like Vedantu's JEE Physics, ensures mastery over convex and concave lenses. Revise linked concepts such as optics, lens, and mirror formula and magnification for a well-rounded understanding. Solid command over theory and diagrams is your path to confidence in JEE optics chapters.
FAQs on Convex and Concave Lenses Explained for JEE Main Physics
1. What is the difference between concave and convex lenses?
Concave and convex lenses differ in shape, light direction, and the types of images they form.
Convex Lens:
- Thicker at the center, thinner at the edges
- Converges parallel rays to a point (focus)
- Can form both real and virtual images
- Used in magnifying glasses, cameras, the human eye
Concave Lens:
- Thinner at the center, thicker at the edges
- Diverges parallel rays outward
- Forms only virtual, diminished images
- Used in spectacles for myopia, peepholes, lasers
2. How do convex and concave lenses form images?
Convex and concave lenses form images by refracting light rays according to their shapes.
- Convex lens: Converges incoming rays to a point, forming real and inverted images when the object is beyond the focus; forms virtual, magnified images when the object is between the lens and its focal point.
- Concave lens: Always diverges rays, creating virtual, erect, and diminished images on the same side as the object.
Ray diagrams help visualize how image position and nature vary with object placement for both lens types.
3. What are the uses of concave lenses?
Concave lenses are widely used in optical devices and everyday applications.
Common uses include:
- Correcting myopia (short-sightedness) in eyeglasses
- Peepholes in doors for wider field viewing
- Part of cameras and telescopes to correct optical aberrations
- In laser systems and scientific instruments for beam divergence control
These uses rely on the diverging property of concave lenses.
4. Is the human eye lens convex or concave?
The human eye lens is a convex lens.
- It is thicker at the center and converges light onto the retina to form real, inverted images.
- Its ability to change shape allows for focusing on objects at different distances (accommodation).
5. Which lens is used to correct myopia and hypermetropia?
Different lenses are used to correct myopia and hypermetropia.
- Concave lens (diverging lens): Corrects myopia (short-sightedness)
- Convex lens (converging lens): Corrects hypermetropia (far-sightedness)
6. Can a concave lens form a real image under any condition?
Concave lenses cannot form real images of real objects, regardless of object position.
- They always produce virtual, erect, and diminished images.
- Only in rare advanced applications (like with converging light from another lens) can a real image be formed, but not in standard school-level scenarios.
7. What mistakes do students make while drawing ray diagrams for lenses?
Common mistakes in lens ray diagrams often include:
- Incorrect arrow directions for refracted rays
- Misplacing the principal focus (F) or optical center (O)
- Mixing up sign conventions (object and image distances)
- Using rules meant for mirrors instead of lenses
To avoid errors, always follow standard ray paths and double-check signs and diagram labeling.
8. What is the lens formula and how is it applied?
The lens formula relates object distance (u), image distance (v), and focal length (f):
1/f = 1/v - 1/u
- Assign signs based on lens type and direction (use the sign convention)
- For convex lens: focal length (f) is positive
- For concave lens: focal length (f) is negative
- Solve for any unknown by substituting known values
9. What is the importance of sign convention in lens problems?
Sign convention for lenses ensures accurate calculation and correct ray tracing.
- Distances measured against the direction of incident light are negative
- For convex lenses, focal length is positive; for concave lenses, it is negative
- Misapplying these conventions can lead to wrong image position and nature
10. Can convex lenses ever form only virtual images?
Convex lenses form a virtual image only when the object is placed between the lens and its focal point (i.e., object distance < focal length).
- The virtual image is erect and magnified, appearing on the same side as the object.
- In all other cases, convex lenses can produce real and inverted images.
