Optics Calculator Lenses, Mirrors & TIR
Calculate focal length, image distance, magnification, critical angle, and lens power with step-by-step solutions. Perfect for GCSE and A-Level Physics.
Thin lens equation: f = focal length, u = object distance, v = image distance
Lens type:
Solve for:
Enter positive value; sign determined by lens type
Always positive
Relates focal length, object distance, and image distance
Same form as lens equation
For spherical mirrors
Ratio of image to object size
For total internal reflection
Power in dioptres, f in metres
For thin lenses in contact
- •Object distance (u): always positive
- •Image distance (v): positive for real image, negative for virtual
- •Focal length (f): positive for converging, negative for diverging
- •Magnification (m): positive for upright, negative for inverted
- •Image height: positive for upright, negative for inverted
Understanding Optics
Optics is the branch of physics that studies the behaviour of light and its interactions with matter. In GCSE and A-Level Physics, you'll focus on geometrical optics, which deals with how light travels through lenses and reflects off mirrors to form images.
The Thin Lens Equation
Focal length (f) = Object distance (u) + Image distance (v) — all as reciprocals
Key concepts include refraction (bending of light at boundaries), reflection (bouncing of light off surfaces), and total internal reflection (complete reflection when light hits a boundary at a steep angle).
Converging (Convex) Lenses
- • Thicker in the middle
- • Positive focal length
- • Can form real or virtual images
- • Used in magnifying glasses, cameras
Diverging (Concave) Lenses
- • Thinner in the middle
- • Negative focal length
- • Always form virtual, upright, diminished images
- • Used in short-sightedness correction
Real vs Virtual Images
Understanding the difference between real and virtual images is essential for optics problems.
Real Images
- • Light rays actually converge at the image point
- • Can be projected onto a screen
- • Always inverted (upside down)
- • Image distance (v) is positive
- • Formed on the opposite side of the lens
Virtual Images
- • Light rays only appear to come from the image
- • Cannot be projected onto a screen
- • Always upright (same way up)
- • Image distance (v) is negative
- • Formed on the same side as the object
Key Optics Formulas
Magnification
Linear magnification tells you how the image size compares to the object. It can be calculated from distances or heights.
|m| > 1 = magnified
|m| < 1 = diminished
m > 0 = upright
m < 0 = inverted
Critical Angle & Total Internal Reflection
TIR occurs when light travels from a denser medium to a less dense medium at an angle greater than the critical angle.
Conditions for TIR: (1) n₁ > n₂ (denser to less dense), (2) angle of incidence > critical angle
Applications: Optical fibres, prisms in binoculars, diamond sparkle, bicycle reflectors, endoscopes
Lens Power & Dioptres
Lens power in dioptres (D) indicates how strongly a lens converges or diverges light. For thin lenses in contact: P_total = P₁ + P₂.
Important: f must be in metres, not cm! A 25 cm lens has power P = 1/0.25 = +4 D, not 1/25 = 0.04 D.
Worked Examples
Practice with these GCSE and A-Level style optics problems:
Example 1: Finding Image Distance
A converging lens has focal length 10 cm. An object is placed 30 cm from the lens. Where is the image formed?
Solution:
Given: f = 10 cm, u = 30 cm, v = ?
Formula: 1/v = 1/f - 1/u
1/v = 1/10 - 1/30 = 3/30 - 1/30 = 2/30
v = 30/2 = 15 cm (real, inverted, diminished)
Example 2: Critical Angle Calculation
Calculate the critical angle for light travelling from glass (n = 1.52) to air (n = 1.00).
Solution:
Step 1: Check TIR condition: 1.52 > 1.00 ✓
Step 2: sin θc = n₂/n₁ = 1.00/1.52 = 0.658
Step 3: θc = sin⁻¹(0.658)
θc = 41.1°
Any angle greater than 41.1° will cause total internal reflection.
Example 3: Combined Lens Power
A converging lens has power +4 D. A diverging lens has power -1 D. What is the combined power and focal length?
Solution:
Given: P₁ = +4 D, P₂ = -1 D
P_total = P₁ + P₂ = +4 + (-1) = +3 D
f = 1/P = 1/3 = 0.333 m = 33.3 cm
P = +3 D (converging), f = 33.3 cm
Example 4: Virtual Image from Diverging Lens
A diverging lens has focal length -15 cm. An object 3 cm tall is placed 30 cm from the lens. Find the image position and size.
Solution:
Step 1: 1/v = 1/f - 1/u = 1/(-15) - 1/30 = -2/30 - 1/30 = -3/30
Step 2: v = -30/3 = -10 cm (virtual image)
Step 3: m = -v/u = -(-10)/30 = +1/3
Step 4: h' = m × h = (1/3) × 3 = 1 cm
Image: 10 cm (same side), virtual, upright, 1 cm tall
Common Mistakes in Optics Problems
Avoid these frequent errors when solving optics questions in GCSE and A-Level Physics exams:
Using cm instead of m for lens power
P = 1/f only works when f is in metres. A 25 cm lens has P = 1/0.25 = +4 D. Using cm gives the wrong answer: 1/25 = 0.04 (not in dioptres!).
Always convert focal length to metres before calculating power. Divide cm by 100.
Forgetting sign convention for focal length
Converging lenses and concave mirrors have positive f. Diverging lenses and convex mirrors have negative f. Mixing these up gives wrong image positions.
Remember: "converging = positive". Write down the sign explicitly before substituting.
Wrong TIR condition
TIR only occurs from denser to less dense medium (n₁ > n₂). Light going from air to glass will NOT undergo TIR — it will refract instead.
Check n₁ > n₂ before using the critical angle formula. If n₁ < n₂, TIR is impossible.
Confusing magnification sign with size
Positive m means upright, negative means inverted. But magnified/diminished depends on |m|, not the sign. A magnification of -3 is inverted AND magnified.
Sign of m = orientation. Magnitude of m = size change. These are independent properties.
Mixing up object distance and image distance
Object distance (u) is always positive for real objects. Image distance (v) can be positive (real) or negative (virtual). Getting them swapped reverses your answer.
u = lens to object (always positive). v = lens to image (positive for real, negative for virtual).
Frequently Asked Questions
How do I know which formula to use?
For image formation: 1/f = 1/u + 1/v. For magnification: m = -v/u or m = h'/h. For critical angle: sin θc = n₂/n₁. For lens power: P = 1/f.
Why is my image distance negative?
A negative v means a virtual image. This happens when the object is inside the focal point (converging lens) or always for diverging lenses.
What's the difference between lens and mirror equations?
Same form (1/f = 1/u + 1/v), but for mirrors there's also f = R/2 where R is radius of curvature.
What is total internal reflection?
Complete reflection of light at a boundary when going from denser to less dense medium at an angle greater than the critical angle.
How do converging and diverging lenses differ?
Converging (convex): thicker in middle, positive f, can form real or virtual images. Diverging (concave): thinner in middle, negative f, always virtual images.
What is lens power measured in?
Dioptres (D). P = 1/f where f is in metres. Positive power = converging, negative = diverging.
How do combined lenses work?
For thin lenses in contact, simply add the powers: P_total = P₁ + P₂. The combined focal length is f = 1/P_total.
Is this calculator suitable for GCSE and A-Level?
Yes! It covers all optics topics including lens/mirror equations, magnification, critical angle, TIR, and lens power with step-by-step solutions.
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