Physics · JEE Advanced only

Combinations of Mirrors and Thin Lenses (JEE Advanced)

Not in the JEE Main syllabus, but it is in JEE Advanced. Study time: about 4 to 6 hours for solid understanding and practice, including sign convention drills and mixed mirror-lens problems.

Last updated: 26 October 2026

Direct answer

Combinations of mirrors and thin lenses involve systems where light passes through multiple optical elements like lenses and mirrors arranged together.

Combinations of mirrors and thin lenses involve systems where light passes through multiple optical elements like lenses and mirrors arranged together. The image formed by one element acts as the object for the next element. You need to track image positions, nature, and magnification through each stage to find the final result.

Official syllabus

What the JEE Advanced syllabus says

“Combinations of mirrors and thin lenses; Magnification”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: combination of thin lenses in contact.

JEE Main focuses mainly on thin lenses in contact sharing a common axis, but Advanced adds mirrors into the mix and tests multi-step problems where light may reflect back through lenses. You must handle sign conventions carefully when switching between refraction and reflection.

Key ideas

What you must understand

Image from first optical element becomes the object for the second element
Total magnification is the product of individual magnifications: m = m₁ × m₂ × m₃...
For lenses in contact, equivalent power P = P₁ + P₂ and 1/f = 1/f₁ + 1/f₂
When a mirror is placed behind a lens, light passes through the lens twice (once before and once after reflection)
Sign convention resets for each new element based on its own pole or optical center
Virtual images can act as real objects for subsequent elements if positioned correctly

Formulas

Formulas and key facts

Mirror formula: 1/v + 1/u = 1/f
Lens formula: 1/v − 1/u = 1/f
Magnification (mirror): m = −v/u
Magnification (lens): m = v/u
Equivalent focal length (lenses in contact): 1/f_eq = 1/f₁ + 1/f₂
Power of combination: P = P₁ + P₂ (in dioptres)
Total magnification: m_total = m₁ × m₂ × m₃...
For silvered lens: P_eq = P_lens + P_mirror + P_lens = 2P_lens + P_mirror

Avoid

Common mistakes

Forgetting to change the object distance sign when image from one element becomes object for the next
Not accounting for the lens being traversed twice when a mirror is placed behind it
Mixing up sign conventions between mirror and lens formulas
Ignoring that magnification can be negative (inverted image) and multiplying only absolute values

Worked example

A JEE Advanced-level example

Question. A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm at a distance of 50 cm apart. A point object is placed 30 cm in front of the lens on the side away from the mirror. Find the position and nature of the final image.

Show solution

For the convex lens: u = −30 cm, f = +20 cm. Using 1/v − 1/u = 1/f: 1/v − 1/(−30) = 1/20, so 1/v = 1/20 − 1/30 = 1/60. Thus v = +60 cm (real image, 60 cm behind lens toward mirror).
This image is 60 cm from lens, but mirror is 50 cm from lens. So image falls 10 cm behind the mirror. For the mirror, this acts as a virtual object: u = +10 cm, f = −10 cm (concave mirror, sign convention with pole as origin).
For concave mirror: 1/v + 1/u = 1/f gives 1/v + 1/10 = 1/(−10), so 1/v = −1/10 − 1/10 = −1/5. Thus v = −5 cm (real image, 5 cm in front of mirror).
This image is now 50 − 5 = 45 cm from the lens. For the lens again: u = +45 cm (object on right side), f = +20 cm. Using 1/v − 1/u = 1/f: 1/v = 1/20 + 1/45 = 13/180. Thus v = 180/13 ≈ 13.8 cm.
Final image is approximately 13.8 cm in front of the lens (on the object side), and it is real.

Answer: Final image is approximately 13.8 cm in front of the lens on the object side, real and inverted.

Solved twice independently; both solutions agree.

FAQs

Frequently asked questions

Is Combinations of Mirrors and Thin Lenses in the JEE Main syllabus?

No. It is in the JEE Advanced 2026 syllabus only. The closest JEE Main topic is combination of thin lenses in contact.

How long does Combinations of Mirrors and Thin Lenses take to prepare for JEE Advanced?

About 4 to 6 hours for solid understanding and practice, including sign convention drills and mixed mirror-lens problems, if you already know the related JEE Main topic.