Thin Lens Equation 1

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Presentation transcript:

Thin Lens Equation 1 𝑢 + 1 𝑣 = 1 𝑓

Terminology The focal length (f) of the lens is the distance from the centre of the lens to the focal point (F). Convex lens (converging)  focal length (f) F 1 𝑢 + 1 𝑣 = 1 𝒇 Concave lens (diverging) Convex lens: f is positive Concave lens: f is negative focal length (f)   F F

Terminology The distance (u) is the distance from the object (O) to the centre of the lens Convex lens (converging)  focal length (f) F O u 1 𝒖 + 1 𝑣 = 1 𝑓 Concave lens (diverging) Convex lens: u is positive O Concave lens: u is positive focal length (f)   u F

Terminology The distance (v) is the distance from the image (I) to the centre of the lens Convex lens (converging)  O u v 1 𝑢 + 1 𝒗 = 1 𝑓 I Concave lens (diverging) For both convex & concave lenses: v is positive if the image is on the opposite side of the lens to the object O I   For both convex & concave lenses: v is negative if the image is on the same side of the lens as the object u F v

Example 1 Calculate the position and magnification of an image formed by a convex lens of focal length 20cm, when a 5cm high object is positioned 30cm in front of the lens.  30 cm v 20 cm O v = ? u = 30 cm f = 20 cm 1 𝑢 + 1 𝒗 = 1 𝑓 I ∴𝑣= 1 𝑓 − 1 𝑢 −1 1 𝒗 = 1 𝑓 − 1 𝑢 𝑣= 1 20 − 1 30 −1 𝑀𝑎𝑔=− 𝑣 𝑢 =− 60 30 =−2 = 60 cm Magnification = x2 (inverted image)

Example 2 Calculate the position and magnification of an image formed by a convex lens of focal length 10cm, when a 5cm high object is positioned 5cm in front of the lens. I  5 cm v 10 cm v = ? u = 5 cm f = 10 cm O 1 𝑢 + 1 𝒗 = 1 𝑓 1 𝒗 = 1 𝑓 − 1 𝑢 𝑀𝑎𝑔=− 𝑣 𝑢 =− −10 5 =+2 ∴𝑣= 1 𝑓 − 1 𝑢 −1 𝑣= 1 10 − 1 5 −1 Magnification = x2 (upright image) = -10 cm

O I  60 cm v 40 cm Example 3 Calculate the position and magnification of an image formed by a concave lens of focal length 40cm, when a 10cm high object is positioned 60cm in front of the lens. v = ? u = 60 cm f = -40 cm 𝑀𝑎𝑔=− 𝑣 𝑢 =− −24 60 =+0.4 Magnification = x0.4 (upright image) 1 𝑢 + 1 𝒗 = 1 𝑓 1 𝒗 = 1 𝑓 − 1 𝑢 ∴𝑣= 1 𝑓 − 1 𝑢 −1 𝑣= 1 −40 − 1 60 −1 = -24 cm

Example 4 Calculate the position and magnification of an image formed by a concave lens of focal length 40cm, when a 10cm high object is positioned 20cm in front of the lens. O I  20 cm v 40 cm v = ? u = 20 cm f = -40 cm 𝑀𝑎𝑔=− 𝑣 𝑢 =− −13.3 20 =+0.67 Magnification = x0.67 (upright image) 1 𝑢 + 1 𝒗 = 1 𝑓 1 𝒗 = 1 𝑓 − 1 𝑢 ∴𝑣= 1 𝑓 − 1 𝑢 −1 𝑣= 1 −40 − 1 20 −1 = -13.3 cm