Formulas

Question 1

Paraxial vergence

Answer 1

L’ = L + F

Question 2

Linear magnification

Answer 2

h’ = h x m or h x L/L’

Question 3

Umbra (point source)

Answer 3

U = h x (L + L’) / L

Question 4

Penumbra

Answer 4

P = s x L’ / L

Question 5

Umbra (extended source)

Answer 5

U = (U + P) - P

Question 6

Image size (extended source)

Answer 6

h’ = (U+P) + P

Question 7

Prentices rule

Answer 7

P = cF

Question 8

Snell’s Law

Answer 8

n Sin i = n’ Sin i’

Question 9

Critical angle

Answer 9

Sin ic = 1 / n

(Given ic) =

n = 1 / sin ic

Question 10

Relative curvature

Answer 10

RC = n old-1 / n new-1

% = (1 - RC) x 100

Question 11

Thin lens theory

Answer 11

F = F1 + F2

Question 12

Velocity/wavelength/frequency

Answer 12

v = f x w

f = v / w

w = v / f

Question 13

Accurate sag

Answer 13

s = r - v(r2 - y2)

Question 14

Approx sag

Answer 14

s = y2 x F / 2000 (n - 1)

Question 15

Power effectivity

Answer 15

F eff = F / 1 - dF

Question 16

n’ (given F, r and n)

Answer 16

n’ = F x r + n

Question 17

Ray trace steps

Answer 17

f = -n / F
L = n / l
L’ = L + F
l’ = n’ / L

h’ = h x L/L’

Question 18

Lateral displacement

Answer 18

t x sin (i1 - i1’) / cos i1’

Question 19

Horizontal displacement

Answer 19

(tan i x t) - (tan i’ x t)

Question 20

Lateral deviation

Answer 20

t x sin (i - i’) / cos i’

Question 21

Apparent depth

Answer 21

BB’ = d x (1 - 1 / n )

Question 22

Angle of deviation

Answer 22

d = i - i’

Question 23

Absolute refractive index

Answer 23

3 x 10ms -1 / velocity of light in a medium

Question 24

Relative refractive index

Answer 24

Velocity of light in medium 1 / velocity of light in medium 2

Question 25

Height of image

Answer 25

h’ = h x L’/L

Question 26

Total deviation

Answer 26

D = d1 + d2
d1 = i1 - i1’
d2 = i2’ - i2

Question 27

Radius (front)

Answer 27

r1 = n’ - 1 / F1

Question 28

Radius (back)

Answer 28

r2 = 1 - n’ / F2

Question 29

Edge thickness

Answer 29

e = t + s

Question 30

Centre thickness

Answer 30

t = e + s

Question 31

Edge thickness (meniscus)

Answer 31

e = t + s2 - s1

Question 32

Centre thickness (meniscus)

Answer 32

t = e + s1 - s2

Question 33

Curved mirrors (step along)

Answer 33

F = r / 2
F = -n / f
L = n / l
L’ = L + F
l’ = -n / L’

h’ = h x L / L’

Question 34

Minimum Plate Thickness (MPT)

Answer 34

S = t - e
F = 2000 (n - 1) x S / y2

Question 35

Image size

Answer 35

h’ = h x L / L’

Question 36

Prentice’s Rule (prismatic effect)

Answer 36

P = cF

Question 37

The tangent scale

Answer 37

Prism dioptres: x = P x y / 100

Degrees of diopters: x = y x tan 1

Degrees of apical angle: d = (n - 1) a
x = y x tan d