Vertical Displacement For Small Angles Calculator

Formula Used:

\[ Vd = pt \times (1 - \frac{1}{RI}) \times (iangle \times \frac{\pi}{180}) \]

Vertical Displacement of Refracted Ray (Vd):

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1. What is Vertical Displacement of Refracted Ray?

Vertical Displacement of Refracted Ray is the vertical distance of the refracted position of the ray from the unrefracted position of the ray on the staff in a parallel plate micrometer. It quantifies how much a light ray is shifted when passing through a transparent medium.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Vd = pt \times (1 - \frac{1}{RI}) \times (iangle \times \frac{\pi}{180}) \]

Where:

\( Vd \) — Vertical Displacement of Refracted Ray (m)
\( pt \) — Plate Thickness (m)
\( RI \) — Refractive Index
\( iangle \) — Angle Of Incidence in degrees
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates how much a light ray is vertically displaced when refracted through a parallel plate, considering the plate's thickness, refractive index, and angle of incidence.

3. Importance of Vertical Displacement Calculation

Details: Accurate calculation of vertical displacement is crucial in optical engineering, lens design, and precision measurement instruments where light path deviations must be accounted for.

4. Using the Calculator

Tips: Enter plate thickness in meters, refractive index (must be ≥1), and angle of incidence in degrees. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is refractive index?
A: Refractive Index is a measure of how much a material can bend or slow down light passing through it compared to the speed of light in a vacuum.

Q2: Why is the angle converted from degrees to radians?
A: Trigonometric functions in mathematical formulas typically use radians rather than degrees, requiring the conversion.

Q3: What are typical values for refractive index?
A: Common values range from 1.0 (vacuum) to about 2.4 (diamond), with most optical glasses around 1.5-1.7.

Q4: Does this formula work for all angles?
A: This formula provides good approximation for small angles. For larger angles, more complex trigonometric calculations may be needed.

Q5: What applications use this calculation?
A: This calculation is used in optical instruments, microscopy, photography, and any system where light passes through transparent materials.