Physics Optics Caluculator

PHOTON OPTICS

FOCAL LENGTH (f) cm OBJECT DISTANCE (u) cm

*Use positive (+) for Convex Lenses.
*Use negative (-) for Concave Lenses.

IMAGE DISTANCE (v)

0.0

MAGNIFICATION (m)

0.0

Type: --

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Optics Calculator

An Optics Calculator is a specialized tool for analyzing the behavior of light. It simplifies complex wave equations to predict how light reflects, refracts, and focuses through lenses and mirrors.

✓ Solves the Lens & Mirror Equation (1/f = 1/v + 1/u)
✓ Calculates Refractive Index using Snell's Law
✓ Determines Magnification & Focal Power
✓ High-precision results for wave-particle physics

REFRACTION

1/f = 1/v + 1/u

OPTICS LIVE

Oat OPTICS

Lens & Mirror Equation

The Lens and Mirror Equation relates the distances of the object and image to the focal length of the optical element. It is the foundation for designing cameras, glasses, and telescopes.

● f: Focal Length (Distance to focus point)
● v: Image Distance (From lens to image)
● u: Object Distance (From lens to object)

Sign Convention: Remember! Distances measured in the direction of light are positive, while those opposite are negative.

1/f = 1/v + 1/u

FOCAL MATH

Magnification (m)

Magnification is the ratio of the image height to the object height. It tells you if the image is enlarged, diminished, or the same size as the actual object.

● m > 1: The image is Enlarged.
● m < 1: The image is Diminished (Smaller).
● Negative m: The image is Inverted (Upside down).

The Math: $m = -v/u$. If you know the distances from the lens, you can find the size of the image!

m = -v / u

ZOOM RATIO

Optical Power (P)

Optical Power measures the degree to which a lens converges or diverges light. It is numerically equal to the reciprocal of the focal length.

● Unit: Measured in Dioptres (D).
● Convex Lens: Positive Power (+).
● Concave Lens: Negative Power (-).

Insight: A "stronger" lens bends light more sharply and has a shorter focal length, resulting in higher Power.

P = 1 / f

DIOPTRE METER

Snell's Law & Index (n)

Snell's Law describes how light bends when passing between different media. The Refractive Index (n) determines the speed and angle of light in that material.

● n: Refractive Index (Air ≈ 1.0, Water ≈ 1.33)
● θ₁: Angle of Incidence (Incoming ray)
● θ₂: Angle of Refraction (Bent ray)

The Law: $n = \frac{\sin(i)}{\sin(r)}$. It explains why a straw looks broken in a glass of water!

n₁sinθ₁ = n₂sinθ₂

SNELL ANALYTICS

The Reciprocal (1/x)

The Reciprocal function, denoted as 1/x, "flips" a number. In optics, it is the mathematical bridge between focal length and optical power.

● Inverse Relation: As x gets larger, 1/x gets smaller.
● Optics Use: Converting focal length (m) to Dioptres.
● Identity: x times its reciprocal always equals 1.

Example: If focal length is 0.5m, the Power is $1 / 0.5 = 2.0$ Dioptres.

1/x

Inverse Function

MATH LOGIC

Snell's Law

n1 sin(θ1) = n2 sin(θ2)

n1, n2 = Refractive Indices

θ1 = Angle of Incidence

θ2 = Angle of Refraction

Optics Formula Reference

Concept	Mathematical Formula	Key Variables
Lens & Mirror	1/f = 1/v + 1/u	u: Object, v: Image, f: Focal length
Magnification	m = -v / u	m: Ratio of image to object size
Optical Power	P = 1 / f	P: Power (Dioptres), f: Meters
Snell's Law	n_1\sin\theta_1 = n_2\sin\theta_2	n: Refractive index, θ: Angles

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Pro Tip: When using the 1/x key on a calculator for the Lens Equation, solve for $1/f$ first, then press 1/x again to find the actual value of $f$.