Lens Power Calculation and Lens Maker's Equation Quiz
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Questions and Answers

What is the unit of measurement of the refractive power of a lens or a surface?

dioptre, denoted as D

What is the sign convention for a lens that adds vergence to light?

plus (+)

What is the medium that light travels in when entering the front surface of a lens?

air (n)

What is the formula for calculating surface power in optics?

<p>F = (n' - n) / r</p> Signup and view all the answers

What is the surface of a lens that light exits through into air after travelling through the lens medium?

<p>back surface</p> Signup and view all the answers

What is the sign convention for the radius of curvature in optics?

<p>A positive sign indicates a convex surface, and a negative sign indicates a concave surface.</p> Signup and view all the answers

What is the purpose of a thin plus lens in optics?

<p>A thin plus lens adds positive vergence to light rays.</p> Signup and view all the answers

What is the power of a lens that adds 2.00D of vergence to light?

<p>+2.00D</p> Signup and view all the answers

What is the condition for defining a plus lens?

<p>Incident vergence must be zero, i.e. parallel rays.</p> Signup and view all the answers

What is the term used to describe the vergence of light leaving the back surface of a lens, which is used to number thick lenses?

<p>back vertex power (BVP)</p> Signup and view all the answers

What is the relationship between the radius of curvature and the unit of measurement in optics?

<p>If the radius of curvature is given in centimetres, a correction of 100 is needed, and if it is given in millimetres, a correction of 1000 is needed.</p> Signup and view all the answers

What is the nominal power of a lens in optics?

<p>The sum of the powers of the individual surfaces of the lens.</p> Signup and view all the answers

What is the sign convention for the radius of curvature of a surface in optics?

<p>A positive sign for the radius of curvature indicates a convex surface, and a negative sign indicates a concave surface.</p> Signup and view all the answers

What is the formula for calculating the nominal power of a thin lens using the lens maker's equation?

<p>The formula is P = (n' - n) * (1/r1 - 1/r2), where P is the nominal power, n' is the refractive index of the medium light is entering, n is the refractive index of the medium light is leaving, r1 is the radius of curvature of the front surface, and r2 is the radius of curvature of the back surface.</p> Signup and view all the answers

What is the surface power of a single surface with a radius of curvature of +20cm, if the refractive index of the medium light is entering is 1.5 and the refractive index of the medium light is leaving is 1.0?

<p>The surface power is +2.50D, calculated using the formula P = (n' - n) / r.</p> Signup and view all the answers

What is the total power of a combination of two thin lenses with nominal powers of +2.00D and +3.00D, placed in contact with each other?

<p>The total power is +5.00D, calculated by adding the nominal powers of the two lenses.</p> Signup and view all the answers

What is the relationship between the focal length of a lens and its nominal power?

<p>The relationship is P = 1/f, where P is the nominal power in dioptres and f is the focal length in metres.</p> Signup and view all the answers

What is the purpose of the lens maker's equation in optics?

<p>The lens maker's equation is used to calculate the nominal power of a thin lens from its refractive index and radius of curvature.</p> Signup and view all the answers

What is the vergence of light rays after passing through a lens that adds +4.00D of power?

<p>+4.00D</p> Signup and view all the answers

What is the point on the optical axis where incident light with zero vergence leaves the lens and then crosses the optical axis?

<p>The secondary focal point (F')</p> Signup and view all the answers

What is the distance from the secondary focal point to the lens, and what is it represented by?

<p>The secondary focal length (f')</p> Signup and view all the answers

What is the purpose of the sign convention in optics, specifically regarding the reference point of the lens?

<p>To determine the direction of the light rays and the vergence added by the lens</p> Signup and view all the answers

What is the difference between the primary focal point (F) and the secondary focal point (F')?

<p>The primary focal point is where rays diverging from a source would have zero vergence when they exit the lens, whereas the secondary focal point is where incident light with zero vergence leaves the lens and then crosses the optical axis</p> Signup and view all the answers

What type of lens would have a positive secondary focal point, and what does it mean?

<p>A plus lens, and it means that the light rays will actually cross at that point</p> Signup and view all the answers

What is the purpose of a lens in optics, and how does it relate to the concept of vergence?

<p>A lens adds vergence to incident light, meaning it changes the direction of light rays. This is achieved through the lens's two polished surfaces, which refract light and alter its path.</p> Signup and view all the answers

Explain the relationship between the focal length of a lens and its nominal power.

<p>The nominal power of a lens is inversely proportional to its focal length. A shorter focal length corresponds to a higher nominal power, and vice versa.</p> Signup and view all the answers

What is the optical axis of a lens, and how does it relate to the primary and secondary focal points/focal lengths?

<p>The optical axis is an imaginary line passing through the center of a lens, perpendicular to its surface. The primary focal point is the point on the optical axis where parallel light rays converge, while the secondary focal point is the point where diverging light rays appear to diverge from.</p> Signup and view all the answers

What is a thin lens, and how is its nominal power calculated given the surface powers?

<p>A thin lens is a lens whose thickness is negligible compared to its radius of curvature. The nominal power of a thin lens can be calculated by adding the surface powers of its front and back surfaces.</p> Signup and view all the answers

How does the power of a lens relate to the curvature of its surfaces?

<p>The power of a lens is dependent on the curvature of its surfaces, with a higher power corresponding to a more curved surface. The sign of the power also depends on the direction of the curvature.</p> Signup and view all the answers

What is the difference between a plus lens and a minus lens, and how do they relate to the concept of vergence?

<p>A plus lens adds vergence to light, causing it to converge, while a minus lens reduces vergence, causing it to diverge. The sign of the lens power determines whether it is a plus or minus lens.</p> Signup and view all the answers

What is the primary purpose of spectacle lenses, and how do they achieve this purpose?

<p>The primary purpose of spectacle lenses is to protect the eye from mechanical/chemical injury and reduce the intensity of incident light. They achieve this by either increasing or decreasing the vergence of incident light, depending on the type of surface.</p> Signup and view all the answers

What is the difference between a convex and concave lens surface, and how do they affect the vergence of incident light?

<p>A convex surface bulges and increases the vergence of incident light, having plus power, whereas a concave surface is hollow and decreases the vergence of incident light, having minus power.</p> Signup and view all the answers

What is the relationship between the radius of curvature of a lens surface and its power?

<p>A surface with a long radius of curvature is flatter and has lower power, while a surface with a short radius of curvature is steeper and has higher power.</p> Signup and view all the answers

What is the purpose of a thin lens in optics, and how does it affect the vergence of incident light?

<p>A thin lens is used to correct vision by either increasing or decreasing the vergence of incident light, depending on the type of lens and its power.</p> Signup and view all the answers

What is the term 'vergence' in optics, and how is it related to the power of a lens?

<p>Vergence refers to the bending of light as it passes through a lens, and the power of a lens determines the amount of vergence it imparts to the incident light.</p> Signup and view all the answers

What is the optical axis of a lens, and how is it related to the lens' power and focal length?

<p>The optical axis is an imaginary line that passes through the center of the lens, and it is the reference point for measuring the lens' power and focal length.</p> Signup and view all the answers

Study Notes

Refractive Power of a Lens

  • The unit of measurement of the refractive power of a lens or a surface is the dioptre, denoted as D (DS for dioptre sphere, DC for dioptre cylinder)
  • The power of a lens (in dioptres) is the reciprocal of the focal length of a lens

Surface Power of a Lens

  • Formula for calculating the surface power of a lens: F = (n' - n) / r, where F is the power in dioptres (D), n is the refractive index of the incident medium, n' is the refractive index of the refracting medium, and r is the radius of curvature of the surface in metres
  • Important to note what optical medium light is currently in and what it will be entering

Lens Terminology

  • Optical axis: An imaginary line that is perpendicular to both sides of the lens, light passes through the optical axis undeviated
  • Thin plus lens: Adds positive vergence to light rays, light rays leaving the lens will now have a positive vergence
  • Types of lenses: Plano-convex, equi-convex, bi-convex, positive meniscus lens

Thin Lenses

  • Lens makers equation: Relates power nominal power of a thin lens to refractive index and radius of curvature
  • Formula for calculating the nominal power of a thin lens: P = (n' - n) (1/r1 - 1/r2), where n' is the refractive index of the medium light is entering, n is the refractive index of the medium light is leaving, r1 is the radius of curvature of the front surface, and r2 is the radius of curvature of the back surface

Focal Length and Vergence

  • Focal length to dioptres: +50cm = +0.5m, R = 1 +0.5 = +2m-1
  • Vergence: The amount of bending of light rays, measured in dioptres
  • Primary focal point (F): The point on the optical axis where rays diverging from a source would have zero vergence when they exit the lens
  • Secondary focal point (F’): The point on the optical axis where incident light (zero vergence) leaves the lens and then crosses the optical axis

Learning Outcomes

  • Define the definition of a lens and the three general functions it performs
  • Recall the three basic types of surface
  • Define the characteristics of plano, convex and concave surfaces
  • Recall the two basic lens forms and their characteristics
  • State the unit of refractive power and how the power of a lens relates to focal length

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Test your knowledge on calculating the nominal power of a thin lens using the Lens Maker's Equation. Understand how to relate power, refractive index, and radius of curvature in lenses.

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