FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Vertical Displacement for Small Angles Formula

Fx Copy

LaTeX Copy

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. Check FAQs

V d = p t \cdot (1 - \frac{1}{RI}) \cdot (i angle \cdot \frac{π}{180})

V_d - Vertical Displacement of Refracted Ray?p_t - Plate Thickness?RI - Refractive Index?i_angle - Angle Of Incidence in degree?π - Archimedes' constant?

Vertical Displacement for Small Angles Example

With values

With units

Only example

Here is how the Vertical Displacement for Small Angles equation looks like with Values.

Here is how the Vertical Displacement for Small Angles equation looks like with Units.

Here is how the Vertical Displacement for Small Angles equation looks like.

19.1842 = 100 \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{3.1416}{180})

19.1842mm = 100mm \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{3.1416}{180})

19.1842 = 100 \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{3.1416}{180})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Engineering » Category

Civil » Category

Surveying Formulas » fx Vertical Displacement for Small Angles

Vertical Displacement for Small Angles Solution

Follow our step by step solution on how to calculate Vertical Displacement for Small Angles?

FIRST Step Consider the formula

V d = p t \cdot (1 - \frac{1}{RI}) \cdot (i angle \cdot \frac{π}{180})

Next Step Substitute values of Variables

∴

V d = 100mm \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{π}{180})

Next Step Substitute values of Constants

∴

V d = 100mm \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{3.1416}{180})

Next Step Convert Units

∴

V d = 0.1m \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{3.1416}{180})

Next Step Prepare to Evaluate

∴

V d = 0.1 \cdot (1 - \frac{1}{1.333}) \cdot (44 \cdot \frac{3.1416}{180})

Next Step Evaluate

∴

V d = 0.0191842192049669m

Next Step Convert to Output's Unit

∴

V d = 19.1842192049669mm

LAST Step Rounding Answer

∴

V d = 19.1842mm

Vertical Displacement for Small Angles Formula Elements

Variables

Constants

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.

Symbol: V_d

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Vertical Displacement of Refracted Ray

Plate Thickness

Plate Thickness is the distance through the bearing plate.

Symbol: p_t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Plate Thickness

Refractive Index

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.

Symbol: RI

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Refractive Index

Angle Of Incidence in degree

Angle Of Incidence in degree is the angle which an incident line or ray makes with a perpendicular to the surface at the point of incidence.

Symbol: i_angle

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Angle Of Incidence in degree

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Tilting level category

Go Angle of Incidence for given Vertical displacement

i angle = (\frac{V d}{p t \cdot (1 - (\frac{1}{RI}))}) \cdot (\frac{180}{π})

Go Refractive Index

RI = \frac{\sin (i angle)}{\sin (r)}

Go Refractive Index given Vertical Displacement

RI = \frac{1}{1 - \frac{V d}{i angle \cdot (\frac{π}{180}) \cdot p t}}

How to Evaluate Vertical Displacement for Small Angles?

Vertical Displacement for Small Angles evaluator uses Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180) to evaluate the Vertical Displacement of Refracted Ray, The Vertical Displacement for Small Angles is defined as the small vertical distance formed due to the rays landed on the plate. This distance is proportional to angle of rotation of the plate. Plate here, is an attachment, sometimes fitted to the tilting levels and precise levels to enable fine readings to be taken. Vertical Displacement of Refracted Ray is denoted by V_d symbol.

How to evaluate Vertical Displacement for Small Angles using this online evaluator? To use this online evaluator for Vertical Displacement for Small Angles, enter Plate Thickness (p_t), Refractive Index (RI) & Angle Of Incidence in degree (i_angle) and hit the calculate button.

FAQs on Vertical Displacement for Small Angles

What is the formula to find Vertical Displacement for Small Angles?

The formula of Vertical Displacement for Small Angles is expressed as Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180). Here is an example- 19184.22 = 0.1*(1-1/1.333)*(44*pi/180).

How to calculate Vertical Displacement for Small Angles?

With Plate Thickness (p_t), Refractive Index (RI) & Angle Of Incidence in degree (i_angle) we can find Vertical Displacement for Small Angles using the formula - Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180). This formula also uses Archimedes' constant .

Can the Vertical Displacement for Small Angles be negative?

Yes, the Vertical Displacement for Small Angles, measured in Length can be negative.

Which unit is used to measure Vertical Displacement for Small Angles?

Vertical Displacement for Small Angles is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Vertical Displacement for Small Angles can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!