DENSER MEDIUM=increased speed

Depth Shallow Deep Wavelength Short Long

Speed Slow Fast

REFLECTION

Angle of incidence =Angle of Refration

REFRACTION (transmission)

𝑠𝑖𝑛𝜃2

𝑠𝑖𝑛𝜃1=𝑣2

𝑣1

𝑠𝑖𝑛𝜃1 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑐𝑒 (1𝑠𝑡)

Direction of propagation

the direction in which the energy is travelling

Wavelength

distance between to poimts in phase

distance between 2 successive crests

Typical tranverse wave

DIVERGING-CONVEX

ALWAYS-Virtual, Erect, Smaller than object

Behind mirror between F and V

Di or f is negative

CONCAVE-CONVERGING

A: Real, Inverted, Smaller, Between C and F

B: Real, Inverted, Same size as object, At C

C: No image, Reflected rays are parallel

D: Virtual, Erect, Larger than object, Behind mirror

𝐷𝑡𝐷𝑎

=ג

1

ג2

=𝑣1

𝑣2=𝑠𝑖𝑛𝜃1

𝑠𝑖𝑛𝜃2=𝐶

𝑣= 𝑛𝐴

𝑛𝐴1 × sin 𝜽𝟏 = 𝑛𝐴2 × sin 𝜽𝟐

𝜽𝟏 = 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑎𝑛𝑔𝑙𝑒

𝜽𝟐 = 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑒𝑑 𝑎𝑛𝑔𝑙𝑒

𝑪 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔𝑕𝑡 𝑖𝑛 𝑣𝑎𝑐𝑢𝑢𝑚(𝑎𝑖𝑟)

𝒗 = 𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔𝑕𝑡 𝑖𝑛 𝑡𝑕𝑎𝑡 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑚𝑒𝑑𝑖𝑢𝑚

𝒏𝑨 = 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑡𝑕𝑎𝑡 𝑚𝑒𝑑𝑖𝑢𝒎

𝒗𝟏 = 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔𝑕𝑡 𝑖𝑛 𝑓𝑖𝑟𝑠𝑡 𝑚𝑒𝑑𝑖𝑢𝑚

𝒗𝟐 = 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔𝑕𝑡 𝑖𝑛 𝑠𝑒𝑐𝑜𝑛𝑑 𝑚𝑒𝑑𝑖𝑢𝑚

𝑫𝒕 = 𝑇𝑟𝑢𝑒 𝑑𝑒𝑝𝑡𝑕

𝑫𝒂 = 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡

DENSER MEDIUM=bends toward the normal and

slower speed for electromagnetic waves

CONVEX-bi convex-CONVERGING

c. Magnified, inverted, real, Di is pos, f is pos

d. Magnified, upright, virtual, Di is neg, f is pos

As an object moves toward F the image increases in size

CONCAVE-bi concave-DIVERGING

a. Diminished, upright, virtual, Di is neg, f is neg

b. Diminished, upright, virtual, Di is neg, f is neg

All measurements are made from the optical centre of

the lens

𝟏

𝒇=𝟏

𝒅𝒐+𝟏

𝒅𝒊

𝒅𝒊 =𝒇𝒅𝒐

(𝒅𝒐 − 𝒇)

𝒅𝒐 =𝒇𝒅𝒊

(𝒅𝒊 − 𝒇)

𝒇 =𝒅𝒊 × 𝒅𝒐

(𝒅𝒐 + 𝒅𝒊)

𝑴 =𝒅𝒊𝒅𝒐

=𝒉𝒊𝒉𝒐

Optical power/ Lens Power 𝟏

𝒇

𝒅𝒊 = 𝒅𝒗 = 𝒗 = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒊𝒎𝒂𝒈𝒆

𝒅𝒐 = 𝒅𝒖 = 𝒖 = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒐𝒇 𝒐𝒃𝒋𝒆𝒄𝒕

𝒉𝒊 = 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒊𝒎𝒂𝒈𝒆

𝒉𝒐 = 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒐𝒃𝒋𝒆𝒄𝒕

Critical Angle-Denser medium to lighter medium

Medium to air 𝐬𝐢𝐧 𝜽𝒄 =𝟏

𝒏𝑨𝒉

𝐬𝐢𝐧𝜽𝒉𝐬𝐢𝐧𝜽𝑳

= 𝒏𝒓 = 𝐬𝐢𝐧𝜽𝒄 =𝒏𝑨𝑳𝒏𝑨𝒉

𝐬𝐢𝐧 𝜽𝒉 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑕𝑒𝑎𝑣𝑖𝑒𝑟 𝑚𝑒𝑑𝑖𝑢𝑚

𝐬𝐢𝐧 𝜽𝑳 =𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑙𝑖𝑔𝑕𝑡𝑒𝑟 𝑚𝑒𝑑𝑖𝑢𝑚

𝒏𝒓 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑎𝑛𝑔𝑙𝑒

𝒏𝑨𝑳 = 𝑎𝑏𝑠𝑜𝑢𝑙𝑢𝑡𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑙𝑖𝑔𝑕𝑡𝑒𝑟 𝑚𝑒𝑑𝑖𝑢𝑚

𝒏𝑨𝒉 = 𝑎𝑏𝑠𝑜𝑢𝑙𝑢𝑡𝑒 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑕𝑒𝑎𝑣𝑖𝑒𝑟 𝑚𝑒𝑑𝑖𝑢𝑚

𝐑 → 𝐎 → 𝐘 → 𝐆 → 𝐁 → 𝐈 → 𝐕

Wavelengths decrease

Refracts more

critical angle decreases

frequency increases

Wavelength of light in a denser medium

𝝀𝒉 =𝝀𝑨𝒏𝒉

For string with mass(m) and length(L) under

tension(F), the speed of the wave is given by

𝑽 = 𝑭𝑳

𝒎

Mark Riley

markriley85@hotmail.com