Vertical Displacement for Small Angles Calculator

✖Plate Thickness is the distance through the bearing plate.ⓘ Plate Thickness [p_t]			+10% -10%
✖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.ⓘ Refractive Index [RI]			+10% -10%
✖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.ⓘ Angle Of Incidence in degree [i_angle]			+10% -10%

✖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.ⓘ Vertical Displacement for Small Angles [V_d]

⎘ Copy

👎

Formula

✖

Vertical Displacement for Small Angles

Formula

`"V"_{"d"} = "p"_{"t"}*(1-1/"RI")*("i"_{"angle"}*pi/180)`

Example

`"19.18422mm"="100mm"*(1-1/"1.333")*("44"*pi/180)`

Calculator

LaTeX

Reset

👍

Download Vertical Control Formula PDF

Vertical Displacement for Small Angles Solution

STEP 0: Pre-Calculation Summary

Formula Used

Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180)
V_d = p_t*(1-1/RI)*(i_angle*pi/180)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Vertical Displacement of Refracted Ray - (Measured in Meter) - 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.
Plate Thickness - (Measured in Meter) - Plate Thickness is the distance through the bearing plate.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Plate Thickness: 100 Millimeter --> 0.1 Meter (Check conversion here)
Refractive Index: 1.333 --> No Conversion Required
Angle Of Incidence in degree: 44 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_d = p_t*(1-1/RI)*(i_angle*pi/180) --> 0.1*(1-1/1.333)*(44*pi/180)

Evaluating ... ...

V_d = 0.0191842192049669

STEP 3: Convert Result to Output's Unit

0.0191842192049669 Meter -->19.1842192049669 Millimeter (Check conversion here)

FINAL ANSWER

19.1842192049669 ≈ 19.18422 Millimeter <-- Vertical Displacement of Refracted Ray

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Civil » Surveying Formulas » Vertical Control » Tilting level » Vertical Displacement for Small Angles

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 4 Tilting level Calculators

Angle of Incidence for given Vertical displacement

Go Angle Of Incidence in degree = (Vertical Displacement of Refracted Ray/(Plate Thickness*(1-(1/Refractive Index))))*(180/pi)

Refractive Index given Vertical Displacement

Go Refractive Index = 1/(1-(Vertical Displacement of Refracted Ray)/(Angle Of Incidence in degree*(pi/180)*Plate Thickness))

Vertical Displacement for Small Angles

Go Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180)

Refractive Index

Go Refractive Index = sin(Angle Of Incidence in degree)/sin(Angle of Refraction)

Vertical Displacement for Small Angles Formula

Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180)
V_d = p_t*(1-1/RI)*(i_angle*pi/180)

Why is Vertical Displacement for Small Angles important in Surveying and Construction?

Vertical Displacement for Small Angles is important because it can cause errors in measurements when leveling instruments are not properly aligned. By understanding the amount of vertical displacement that occurs for a given angle of tilt, surveyors and construction workers can make adjustments to their measurements and ensure that their work is accurate.

How to Calculate Vertical Displacement for Small Angles?

Vertical Displacement for Small Angles calculator uses Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180) to calculate 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 calculate Vertical Displacement for Small Angles using this online calculator? To use this online calculator 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. Here is how the Vertical Displacement for Small Angles calculation can be explained with given input values -> 19184.22 = 0.1*(1-1/1.333)*(44*pi/180).

FAQ

What is Vertical Displacement for Small Angles?

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 and is represented as V_d = p_t*(1-1/RI)*(i_angle*pi/180) or Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180). Plate Thickness is the distance through the bearing plate, 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 & 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.

How to calculate Vertical Displacement for Small Angles?

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 is calculated using Vertical Displacement of Refracted Ray = Plate Thickness*(1-1/Refractive Index)*(Angle Of Incidence in degree*pi/180). To calculate Vertical Displacement for Small Angles, you need Plate Thickness (p_t), Refractive Index (RI) & Angle Of Incidence in degree (i_angle). With our tool, you need to enter the respective value for Plate Thickness, Refractive Index & Angle Of Incidence in degree and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search