An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed.
Converging lens means a convex lens. As the distances given in the question are large, so we choose a scale of 1: 5, i.e., 1 cm represents 5 cm. Therefore, on this scale 5 cm high object, object distance of 25 cm and focal length of 10 cm can be represented by 1 cm high, 5 cm and 2 cm lines respectively. Now, we draw the ray diagram as follows:(i) Draw a horizontal line to represent the principal axis of the convex lens.(ii) Centre line is shown by DE.(iii) Mark two foci F and F' on two sides of the lens, each at a distance of 2 cm from the lens.(iv) Draw an arrow AB of height 1 cm on the left side of lens at a distance of 5 cm from the lens.(v) Draw a line AD parallel to principal axis and then, allow it to pass straight through the focus (F') on the right side of the lens.(vi) Draw a line from A to C (centre of the lens), which goes straight without deviation.(vii) Let the two lines starting from A meet at A'.(viii) Draw AB', perpendicular to the principal axis from A'.(ix) Now AB', represents the real, but inverted image of the object AB.(x) Then, measure CB' and A'B'. It is found that CB' = 3.3 cm and A'B' = 0.7 cm.
(xi) Thus the final position, nature and size of the image A'B' are: (a) Position of image A'B' = 3.3 cm × 5 = 16.5 cm from the lens on opposite side. (b) Nature of image A’B’: Real and inverted.
(c) Height of image A'B': 0.7 × 5 = 3.5 cm, i.e., image is smaller than the object.
The refractive index of glass with respect to air is `3/2` and the refractive index of water with respect to air is `4/3`. The refractive index of glass with respect to water will be:
(a) 1.525
(b) 1.225
(c) 1.425
(d) 1.125
1.125 Explanation:
Refractive index of glass with respect to water = `"Refractive index of glass with respect to air"/"Refractive index of water with respect to air "`
`(3/2)/(4/3)`
=1.125
Concept: Refractive Index
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Option 4 : 2.25 × 108 m/s
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10 Questions 40 Marks 10 Mins
CONCEPT:
Refractive index:
- The ratio of the speed of light in a vacuum to the speed of light in a medium is called the refractive index of that medium.
- It is also called an absolute refractive index.
\({\rm{Refractive\;index\;}}\left( μ \right) = {\rm{\;}}\frac{{Speed\;of\;light\;in\;vaccum\left( C \right)}}{{Speed\;of\;light\;in\;a\;medium\left( v \right)}}\)
EXPLANATION:
Given - Refractive index of glass (μg) = 3/2, refractive index of water (μw) = 4/3 and speed of light in glass (vg) = 2 x 108 m/s,
- Mathematically the refractive index can be written as
\(⇒ {Speed\;of\;light\;in\;a\;medium\left( v \right)} = {\rm{\;}}\frac{{Speed\;of\;light\;in\;vaccum\left( C \right)}}{{\rm{Refractive\;index\;}}\left( μ \right)}\)
- As we know the speed of light in a vacuum is constant, therefore the product of the speed of light in a medium and refractive index is constant. Hence
⇒ Speed of light in a medium (v) × refractive index (μ) = constant
⇒ vg × μg = vw × μw
\(⇒ v_w=\frac{v_g× \mu_g}{\mu_w}=\frac{2× 10^8× \frac{3}{2}}{\frac{4}{3}}\)
⇒ vw = 2.25 × 108 m/s
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The refractive index of water is 4 / 3 and that of glass is 3 / 2 . Calculate the refractive index of glass with respect to water.
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