Chapter 5: Spherical lenses

Question 1

What are 3 types of a) convex and b) concave lenses?

Answer 1

1. bi-convex (/bi-concave)
2. plano-convex (/plano-concave)
3. convex meniscus (/concave meniscus)

Question 2

What is the total vergence power of most lenses used in ophthalmology?

Answer 2

depends on vergence power of each surface and the thickness of the lens

most lenses are thin leses, so total power is sum of the two surface powers

Question 3

What is the nodal point in spherical lens diagrams?

Answer 3

the point at which the principal plane (vertical line representing lens) and the principal axis (horizontal line bisecting lens) cross

rays of light pass through this point undeviated

Question 4

What is the principal focus, F, of a spherical lens?

Answer 4

light paralell to the principal axis is converged to (convex lenes) or diverged from (concave lens) the point F

there is a principal focus on each side of the lens, equidistant from the nodal point

Question 5

What is the sign in front of the value of f₂ for concave vs convex lenses?

Answer 5

f₂ positive for convex lens, negative for concave

Question 6

What is formula to calculate the distance of an image from the principal point from a spherical lens?

Answer 6

1/v - 1/u = 1/f₂

v=distance of image from principal point, u=distnace of object from principal point, f₂ is second focal length

Question 7

What are the 2 rays needed to construct an image of an object through a spherical lens?

Answer 7

• line from top of object through nodal point, passes undeviated
• line from top of object, passes parallel to principal axis then is is deviated to f₂ (convex) or away from f₂ (concave)

Question 8

What are the properties of an image of an object if it is outside f₁ for a convex lens?

Answer 8

real, inverted, outside f₂

Question 9

What are the properties of an image of an object if it is inside f1 for a convex lens?

Answer 9

virtual, erect, magnified, further from the lens than object (outside f₁)

Question 10

What are the properties of an image of an object if it is at f₁ for a convex lens?

Answer 10

virtual, erect, at infinity (the lines are parallel)

Question 11

What are the properties of an image of an object at any position for a concave lens?

Answer 11

(like the convex mirror it’s the weird one)

virtual, erect, diminished image inside f₂

Question 12

How does focal length relate to power of a lens?

Answer 12

shorter focal length = more powerful lens

Question 13

What is the mathematical equation linking lens power and focal length?

Answer 13

unit of lens power = reciprocal of second focal length

F = 1/f₂

F= vergence power of lens in dioptres, f₂ is second focal length in metres

Question 14

What is the equation to claculate linear magnification produced by a spherical lens?

Answer 14

Linear magnification = I/O = v/u

I=image size, O=object size, v=distance of image from principal plane, u=distance of object from principal plane

Question 15

What is the key measure which governs the retinal image size of an object?

Answer 15

the angle subtended at the eye

Question 16

What is the equation used to calculate apparent image size?

Answer 16

apparent image size = object (or image) size / distance from eye = tanθ

Question 17

Which position of an object will produce an image at infinity and how does angular magnification play a useful role?

Answer 17

object at the first principal focus for a convex lens will produce image at infinity

the object and its infinitely distant iamge subtend the same angle θ, at the lens and the eye (if eye very cloes to lens)

angular magnification is therefore unity - apparent object size and apparent image size are the same

Question 18

How can the magnifying power of a convex lens for an image very close to the eye be calculated?

Answer 18

magnifying power = apparent size of image / apparent size of object at 25cm from the eye

M = F / 4

where M = magnifying power, F = power of the lens in dioptres (because 25cm = 0.25m)

Question 19

What is the lens power of the commonly used x8 magnification loupe?

Answer 19

M = F/4

8 = F/4

F = +32 dioptres

Question 20

What type of lens is a magnifying loupe formed from?

Answer 20

convex lens

Question 21

What happens to light incident on a lens outside its axial zone?

Answer 21

deviated towards (convex lens) or away from (concave lens) the axis

peripheral portion of the lens acts as a prism

refracting angle between lens surface grows larger as the edge of the lens is approached - prismatic effect increases towards periphery of the lens

Question 22

What is the definition of decentration of a lens?

Answer 22

use of a non-axial portion of a lens to gain prismatic effect

Question 23

What is the formula to calculate prismatic power of a lens?

Answer 23

P = F x D

P = prismatic power in prism dioptres, F = lens power in dioptres, D = decentration in centimetres

Question 24

What is the underlying mechanism of spherical aberration?

Answer 24

increasing prismatic power of the more peripheral parts of a spherical lens

Question 25

What are 2 troublesome effects of the prismatic effect in high-power spectacle lenses?

Answer 25

1. jack-in-the-box effect
2. ring scotoma