Question 1 :
A ray is incident at an angle 6<sup>0</sup> on side AB of a small angle prism ABC, of prism angle 3<sup>0</sup>. If r<sub>1</sub> and r<sub>2</sub> are the angles made by ray inside the prism with normals of side AB and AC respectively, then (r<sub>1</sub> + r<sub>2</sub>) is :
Question 2 :
A thin lens made of glass of refractive index {tex} \mu = 1.5 {/tex} has a focal length equal to {tex} 12 \mathrm { cm } {/tex} in air. It is now immersed in water {tex} \left( \mu = \frac { 4 } { 3 } \right) . {/tex} Its new focal length is<br>
Question 4 :
Two thin lens have a combined power of 10 D in contact. When separated by 20 cm their equivalent power is 6.25 D. Find their individual powers in dioptres -
Question 5 :
What will be the angular width of central maxima in Fraunhoffer diffraction when light of wavelength {tex} 6000 A ^{\circ}{/tex} is used and slit width is 12 X {tex}10^-5{/tex}<br>is {tex} 12 \times 10 ^ { - 5 } \mathrm { cm } {/tex}<br>
Question 6 :
An object 1 cm tall is placed in front of a mirror at a distance of 4 cm. In order to produce an upright image of 3cm height one needs a
Question 7 :
A simple telescope, consisting of an objective of focal length 30 cm and a single eye lens of focal length 6 cm. Eye observes final image in relaxed condition. If the angle subtended on objective is 1.5º then image will subtend angle of
Question 8 :
A thin rod of length 10 cm is placed along the axis of a concave mirror of focal length 30 cm such that its real diminished image just touches the rod. What is the length of the rod image?
Question 9 :
A microscope has an objective of focal length {tex}1.5 \mathrm { cm } {/tex} and an eye-piece of focal length {tex} 2.5 \mathrm { cm } . {/tex} If the distance between objective and eye-piece is {tex} 25 \mathrm { cm } , {/tex} what is the approximate value of magnification produced for relaxed eye?
Question 10 :
Magnification produced by astronomical telescope for normal adjustment is 10 and length of telescope is 1.1 m. The magnification when the image is formed at least distance of distinct vision (D = 25 cm) is -
Question 11 :
An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror (in cm) is
Question 12 :
A bulb is placed at a depth of {tex}2 \sqrt { 7 } \mathrm { m } {/tex} in water and a floating opaque disc is placed over the bulb so that the bulb is not visible from the surface. The radius of the disc should be at least {tex} \left( \mu _ { \text {water } } = 4 / 3 \right) {/tex}
Question 13 :
The relation between lateral magnification <em>m</em>, object distance <em>u</em> and focal length <em>f</em> of a spherical mirror is
Question 14 :
Consider telecommunication through optical fibres. Which of the following statements is not true?
Question 15 :
A thin film of thickness <em>t</em> and index of refraction 1.33 coats a glass with index of refraction 1.50. Which of the following thickness <em>t</em> will not reflect normally incident light with wavelength 640 nm in air?
Question 16 :
A double convex lens is made of glass of refractive index {tex} 1.5 . {/tex} If its focal length is {tex} 30 \mathrm { cm } , {/tex} then radius of curvature of each of its curved surface is<br>
Question 17 :
Two thin lenses whose powers are {tex} + 2 D {/tex} and {tex} - 4 D {/tex} respectively combine, then the power of combination is
Question 18 :
An astronomical telescope in normal adjustment receives light from a distant source S. The tube length is now decreased slightly -
Question 19 :
A plane glass slab is kept over various coloured letters, the letter which appears least raised is
Question 20 :
A small metallic spherical ball is placed little away from the centre of a large concave mirror of radius of curvature 2.5 cm. When the ball is released, it begins to oscillate, in SHM with time period- (g = 10 m/s<sup>2</sup>)
Question 21 :
A star is moving towards the earth with a speed of {tex} 4.5 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s } {/tex}. If the true wavelength of a certain line in the spectrum received from the star is {tex} 5890 \mathrm { A } {/tex}, its apparent wavelength will be about {tex}[c = 3 \times 10^{8} m/s]{/tex}<br>{tex} \left[ c = 3 \times 10 ^ { 8 } m / s \right] {/tex}<br>
Question 22 : Two plane mirrors <em>A</em> and <em>B</em> are aligned parallel to each other as shown in figure. A light ray is incident at an angle of 30<font face="Symbol">°</font> at a point just inside one end of <em>A</em>. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c80b1da6d070c2abfb53"/>
Question 23 : A thin isosceles prism with angle 4<sup>0</sup> and refractive index 1.5 is placed inside a transparent tube with water {tex}\left( \text{refractive}\ \text{index} = \frac{5}{4} \right){/tex}as shown. The deviation of light due to prism will be <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c848bfef6349df010031"/>
Question 24 :
The plane face of plano-convex lens of focal length 20 cm is silvered. This combination is equivalent to the type of mirror and its focal length is
Question 25 : A cylinder is filled with a liquid of refractive index <font face="Symbol">µ</font>. The radius of the cylinder is decreasing at a constant rate <em>K</em>. The volume of the liquid inside the container remains constant at <em>V</em>. The observer and the object <em>O</em> are in a state of rest and at a distance <em>L</em> from each other. The apparent velocity of the object as seen by the observer, (when radius of cylinder is <em>r</em>) <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c865bfef6349df01005a"/>
Question 26 : In the given situation, what is the angle of deviation?<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5bb3545637834a588987c9"><br>
Question 27 :
Focal length of an equiconvex lens is {tex} 20 \mathrm { cm } . {/tex} If we cut it once perpendicular to principle axis, and then along principal axis, then focal length of each part will be
Question 28 :
The plane face of plano-convex lens of focal length 20 {tex} \mathrm { cm } {/tex} is silvered. This combination is equivalent to the type of mirror and its focal length is
Question 29 :
An observer looks at a distant tree of height {tex}10\, \mathrm { m } {/tex} with a telescope of magnifying power of {tex} 20 . {/tex} To the observer the tree appears:
Question 30 : A ray of light from a liquid {tex} ( \mu = \sqrt { 3 } ) {/tex} is incident on a system of two right-angled prisms of refractive indices {tex} \sqrt { 3 } {/tex} and {tex} \sqrt { 2 } {/tex} as shown. The ray suffers zero deviation when emerges into air from {tex} C D . {/tex} The angle of incidence {tex} i {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5bb3005637834a58898786"><br>
Question 31 :
A car is fitted with a convex side-view mirror of focal length {tex} 20 \mathrm { cm } . {/tex} A second car {tex}2.8 \mathrm { m } {/tex} behind the first car is overtaking the first car at a relative speed of {tex}15\, \mathrm { m } / \mathrm { s } {/tex} . The speed of the image of the second car as seen in the mirror of the first one is:
Question 32 :
A light wave of frequency $5 \times 10^{14} Hz$ passes through a medium of refractive index 2.4. Its wavelength in the medium will be:<br/>
Question 33 :
A commonly used lens coating material is $MgF_2$ with $n=1.38.$ Find the thickness of non-reflective coating, one shall have for $550nm$ light if it is applied to glass of $n=1.52.$
Question 34 : A glass prism of refractive index 1.5 is immersed in water (<font face="Symbol">µ</font> = 4/3). A light beam incident normally on the face <em>AB</em> is totally reflected to reach the face <em>BC</em>, if <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c81b4bec8070e4e15297"/>
Question 35 : An object {tex} O {/tex} is placed in front of a small plane mirror {tex} M _ { 1 } {/tex} and a large convex mirror {tex} M _ { 2 } {/tex} of focal length {tex} f {/tex}. The distance between {tex} O {/tex} and {tex} M _ { 1 } {/tex} is {tex} x , {/tex} and the distance between {tex} M _ { 1 } {/tex} and {tex} M _ { 2 } {/tex} is {tex} y . {/tex} The images of {tex} O {/tex} formed by {tex} M _ { 1 } {/tex} and {tex} M _ { 2 } {/tex} coincide. The magnitude of {tex} f {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5bb3465637834a588987bd"><br>
Question 36 : A light ray falls on a square slab at an angle 45<font face="Symbol">°</font>. What must be the minimum index of refraction of glass, if total internal reflection takes place at the vertical face? <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c8261da6d070c2abfb69"/>
Question 37 :
A thin film of thickness {tex} t {/tex} and index of refraction {tex}1.33{/tex} coats a glass with index of refraction {tex} 1.50 . {/tex} Which of the following thickness {tex} t {/tex} will not reflect normally incident light with wavelength {tex} 640 \mathrm { nm } {/tex} in air?<br>
Question 38 : η number of identical equilateral prisms are kept in contact as shown in figure. If deviation through a single prism is δ then consider the following statements (m is an integer). (i) if (η = 2m) deviation through η prisms is zero (ii) if (η = 2m + 1) deviation through system of η prisms is δ (iii) if η = 2m deviation through system of η prisms is δ (iv) if η = 2m + 1 deviation through system of η prisms is zero <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c857bfef6349df010048"/>
Question 39 : Light is incident normally on face {tex} A B {/tex} of a prism as shown in Fig. A liquid of refractive index {tex} \mu {/tex} is placed on face {tex} A C {/tex} of the prism. The prism is made of glass of refractive index {tex} 3 / 2 . {/tex} The limits of {tex} \mu {/tex} for which total internal reflection cannot takes place on face {tex} A C {/tex} is<br><br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e8acd07fe2ff92479fb1880' class="uploaded-image" />
Question 40 : In a converging lens of focal length <em>f</em> and the distance between real object and its real image is 4<em>f</em>. If the object moves <em>x</em><sub>1</sub> distance towards lens its image moves <em>x</em><sub>2</sub> distance away from the lens and when object moves <em>y</em><sub>1</sub> distance away from the lens its image moves <em>y</em><sub>2</sub> distance towards the lens, then choose the correct option <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c83bbfef6349df010027"/>
Question 41 : An equiconvex lens made up of a material of refractive index 1.5 has focal length of 10 cm when placed in air as shown in the figure. One side of the medium is replaced by another medium of refractive index 1.3. If <em>X</em> and <em>Y</em> are the image distances when the object is placed at a distance of 20cm from optical centre in the medium with refractive index 1 and 1.3 respectively, then <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16c868bfef6349df01005d"/>
Question 42 :
For a concave mirror of focal length {tex} 20 \mathrm { cm } , {/tex} if the object is at a distance of {tex}30 \mathrm { cm } {/tex} from the pole, then the nature of the image and its magnification will be
Question 43 :
We have two equilateral prisms {tex} A {/tex} and {tex} B . {/tex} They are made of materials having refractive index 1.5 and 1.6. For minimum deviation, incident angle will be
Question 44 :
Two point white dots are {tex} 1\,\mathrm { mm } {/tex} apart on a black paper. They are viewed by eye of pupil diameter {tex} 3\,\mathrm { mm } {/tex} . Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light = {tex} 500 \mathrm { nm } {/tex}]
Question 45 :
A thin film of thickness {tex}\mathrm t {/tex} and index of refraction {tex}1.33{/tex} coats a glass with index of refraction {tex} 1.50 . {/tex} Which of the following thickness {tex}\mathrm t {/tex} will not reflect normally incident light with wavelength {tex} 640\mathrm { nm } {/tex} in air?
Question 46 :
The refractive index of a certain glass is $1.5$ for light where wavelength in vacuum is $6000 A^o V$ The wavelength of this light when it passes through the glass is ___________.
Question 47 :
In vacuum, to travel distance 'd', light takes time 't' and in medium to travel distance $'5d'$, it takes time 'T'. The critical angle of the medium is.<br>
Question 48 :
A water film is formed on a glass-block. A light ray is incident on water film from air at an angle of $\displaystyle { 60 }^{ \circ }$ with the normal. The angle of incidence on glass slab is<br>($\displaystyle { \mu }_{ g } = 1.5,{ \mu }_{ w } = \frac { 4 }{ 3 } $)
Question 49 :
If refractive index of a slab varies as $m = 1 + x^2$ is measured from one end, then optical path length of a slab of thickness 1 m is
Question 50 :
Air has refractive index $1.0003$. Find the thickness of air column which will contain one more wavelength of yellow light of $6000$ $A^0$ than in same thickness of vacuum.
