Optics

81. If the image of an object, formed by a concave mirror is virtual, erec

If the image of an object, formed by a concave mirror is virtual, erect and magnified, then the object is placed

[amp_mcq option1=”at the principal focus” option2=”at the centre of curvature” option3=”beyond the centre of curvature” option4=”between the pole of the mirror and the principal focus” correct=”option4″]

This question was previously asked in
UPSC NDA-2 – 2016
Download PDFAttempt Online
A concave mirror forms a virtual, erect, and magnified image when the object is placed between its pole (P) and principal focus (F). In this position, rays from the object diverge after reflection and appear to originate from a point behind the mirror, forming a virtual image.
Image formation by a concave mirror depends on the object’s position. A virtual, erect, and magnified image is formed when the object is within the focal length (between P and F).
When the object is placed at the principal focus, the image is formed at infinity (real, inverted, highly magnified). When the object is at the centre of curvature, the image is also at the centre of curvature (real, inverted, same size). When the object is beyond the centre of curvature, the image is formed between the principal focus and the centre of curvature (real, inverted, diminished).

82. Which one of the following statements is not correct ?

Which one of the following statements is not correct ?

[amp_mcq option1=”The longest wavelength of light visible to human eye is about 700 nm” option2=”The shortest wavelength of light visible to human eye is about 400 nm” option3=”The wavelength of gamma rays is longer than that of X-rays” option4=”The ability of a telescope to form separable images of close objects is called its resolving power” correct=”option3″]

This question was previously asked in
UPSC NDA-2 – 2016
Download PDFAttempt Online
The electromagnetic spectrum is ordered by wavelength (or frequency/energy). Moving from shorter wavelengths to longer wavelengths, the order is typically Gamma rays, X-rays, Ultraviolet, Visible light, Infrared, Microwaves, Radio waves. Therefore, gamma rays have shorter wavelengths than X-rays. The statement that the wavelength of gamma rays is longer than that of X-rays is incorrect.
Order of electromagnetic spectrum components by increasing wavelength: Gamma < X-ray < UV < Visible < IR < Microwave < Radio.
Statements A and B are correct descriptions of the approximate range of wavelengths for visible light, with red light (around 700 nm) having the longest wavelength and violet light (around 400 nm) having the shortest. Statement D provides a correct definition of resolving power, which is an important characteristic of optical instruments.

83. When a ray of light enters a glass slab, then

When a ray of light enters a glass slab, then

[amp_mcq option1=”only the frequency changes” option2=”frequency and velocity change” option3=”frequency does not change” option4=”frequency and wavelength change” correct=”option3″]

This question was previously asked in
UPSC NDA-2 – 2016
Download PDFAttempt Online
When light passes from one medium to another (like air to glass), its speed changes, and its wavelength changes. However, the frequency of the light, which is determined by the source, remains constant.
The speed of light ($v$), frequency ($f$), and wavelength ($\lambda$) are related by the equation $v = f\lambda$. When light enters a denser medium, its speed decreases. Since frequency ($f$) is constant, the wavelength ($\lambda = v/f$) must decrease proportionally.
The change in speed and wavelength leads to the phenomenon of refraction, where the light ray bends at the interface between the two media (unless it enters perpendicularly). The energy of the light is also proportional to its frequency (E = hf), so frequency remaining constant means the energy of each photon is conserved.

84. Which one of the following statements is correct?

Which one of the following statements is correct?

[amp_mcq option1=”The image formed by a concave mirror for an object lying at infinity is at the principal focus, highly diminished, real and inverted.” option2=”A ray of light parallel to the principal axis after reflection from a concave mirror appears to diverge from the principal focus of the mirror.” option3=”The focal length of a spherical mirror is double of its radius of curvature.” option4=”A ray of light travelling from a rarer medium to a denser medium bends away from the normal.” correct=”option1″]

This question was previously asked in
UPSC NDA-2 – 2015
Download PDFAttempt Online
Let’s analyze each statement:
A) The image formed by a concave mirror for an object lying at infinity is indeed formed at the principal focus (F), is highly diminished (essentially a point image), and is real and inverted. This statement accurately describes the image formation for a concave mirror when the object is at infinity.
For a concave mirror, when an object is placed at infinity, the rays coming from it are parallel to the principal axis and converge at the principal focus after reflection, forming a real, inverted, and highly diminished image.
B) A ray parallel to the principal axis after reflection from a concave mirror passes *through* the principal focus, it does not appear to diverge from it. This description applies to a convex mirror.
C) The focal length (f) of a spherical mirror is half of its radius of curvature (R), i.e., f = R/2. The statement says it is double, which is incorrect.
D) A ray of light travelling from a rarer medium to a denser medium bends *towards* the normal, not away from it. Bending away from the normal occurs when light travels from a denser medium to a rarer medium.
Therefore, only statement A is correct.

85. Which one of the following statements is not correct?

Which one of the following statements is not correct?

[amp_mcq option1=”The radius of curvature of a concave mirror is twice its focal length” option2=”Power of a convex lens is negative and that of a concave lens is positive” option3=”The radius of curvature of a plane mirror is infinity” option4=”When a ray of light passes from an optically denser medium to an optically rarer medium, the angle of refraction is greater than the corresponding angle of incidence” correct=”option2″]

This question was previously asked in
UPSC NDA-2 – 2015
Download PDFAttempt Online
The correct answer is B. The statement about the power of convex and concave lenses is incorrect.
– Statement A is correct. For a spherical mirror, the radius of curvature (R) is twice the focal length (f), i.e., R = 2f.
– Statement B is incorrect. The power of a lens (P = 1/f) is positive for a converging lens (convex lens) because its focal length (f) is positive. The power of a diverging lens (concave lens) is negative because its focal length (f) is negative.
– Statement C is correct. A plane mirror can be considered as a part of a spherical mirror with an infinite radius of curvature. Consequently, its focal length (f = R/2) is also infinite.
– Statement D is correct. According to Snell’s Law, when light travels from a denser medium (higher refractive index n₁) to a rarer medium (lower refractive index n₂), it bends away from the normal. This means the angle of refraction (θ₂) is greater than the angle of incidence (θ₁), as n₁ sin θ₁ = n₂ sin θ₂ and n₁ > n₂, implies sin θ₂ > sin θ₁, leading to θ₂ > θ₁.
The power of a lens is a measure of its ability to converge or diverge light rays. It is expressed in dioptres (D), where 1 D = 1 m⁻¹. Convex lenses are used to correct hypermetropia (long-sightedness), and concave lenses are used to correct myopia (short-sightedness).

86. In case of a compound microscope which of the following statements is

In case of a compound microscope which of the following statements is / are correct?

  • 1. The focal length of the eye piece is larger than the focal length of the objective
  • 2. The focal length of the eye piece is smaller than the focal length of the objective
  • 3. The image produced in a normal optical microscope is real
  • 4. The image produced in a normal optical microscope is virtual

Select the correct answer using the code given below:

[amp_mcq option1=”1 only” option2=”1 and 4″ option3=”2 and 3″ option4=”2 and 4″ correct=”option2″]

This question was previously asked in
UPSC NDA-2 – 2015
Download PDFAttempt Online
The correct answer is B. Statements 1 and 4 are correct for a compound microscope.
– Statement 1 is correct. In a compound microscope, the objective lens typically has a very short focal length to produce a highly magnified intermediate image. The eyepiece lens acts as a magnifying glass for this intermediate image and usually has a longer focal length than the objective.
– Statement 2 is incorrect. The focal length of the eyepiece is typically larger than that of the objective.
– Statement 3 is incorrect. The final image produced by a compound microscope and viewed by the observer is a virtual image. The objective lens forms a real intermediate image, but the eyepiece forms a virtual image of this intermediate image.
– Statement 4 is correct. The final image observed through the eyepiece of a compound microscope is virtual, magnified, and inverted relative to the original object.
A compound microscope uses two lens systems to achieve high magnification. The total magnification is the product of the magnification of the objective and the eyepiece. The intermediate image formed by the objective is real, magnified, and inverted, located within the focal length of the eyepiece. The eyepiece then produces a final, further magnified, virtual, and inverted image.

87. Which of the following statements with regard to the phenomenon of the

Which of the following statements with regard to the phenomenon of the primary rainbow formation by water droplets is/are correct ?

  • 1. It involves refraction and one internal reflection of sunlight.
  • 2. It involves refraction of sunlight only.
  • 3. It is formed as the inner bow.
  • 4. It may involve more than one internal reflection as well as refraction of sunlight.

Select the answer using the code given below :

[amp_mcq option1=”1 only” option2=”1 and 3″ option3=”3 and 4″ option4=”2 and 3″ correct=”option2″]

This question was previously asked in
UPSC NDA-1 – 2024
Download PDFAttempt Online
The formation of a primary rainbow involves sunlight entering a water droplet, undergoing refraction at the front surface, reflecting internally off the back surface, and then refracting again as it exits the front surface. This process disperses the white light into its constituent colors. Statement 1 correctly describes this as involving refraction and one internal reflection. The primary rainbow appears as the inner and brighter bow in the sky, formed by deviation angles around 40-42 degrees relative to the direction opposite the sun. Statement 3 correctly identifies it as the inner bow. Statement 2 is incorrect as reflection is crucial. Statement 4 describes the formation of secondary or higher-order rainbows, not the primary rainbow, which specifically involves a single internal reflection.
– Primary rainbow involves one internal reflection and two refractions of sunlight within water droplets.
– Primary rainbow is the brighter, inner bow observed in the sky.
– Different colors are deviated by different angles due to dispersion during refraction.
The secondary rainbow, which is fainter and appears outside the primary bow (at angles around 50-53 degrees), is formed by sunlight undergoing two internal reflections within the water droplet. The order of colors is reversed in the secondary rainbow compared to the primary one.

88. For a human eye, where u is the distance of an object from the eye, f

For a human eye, where u is the distance of an object from the eye, f is the focal length of the lens and v is the distance of image from the eye, which is the correct schematic graph ?

[amp_mcq option1=”[Graph (v vs u)]” option2=”[Graph (v vs u)]” option3=”[Graph (f vs u)]” option4=”[Graph (v vs f)]” correct=”option3″]

This question was previously asked in
UPSC NDA-1 – 2024
Download PDFAttempt Online
The correct schematic graph for the human eye shows how the focal length (f) of the lens changes with the distance of the object (u). The distance of the image (v) from the lens to the retina is constant in a healthy eye. The lens formula relating these quantities is 1/f = 1/v + 1/u (using magnitudes for a convex lens forming a real image). Since v is constant, as the object distance u increases, 1/u decreases. For the equality to hold, 1/f must also decrease, which means f must increase. Conversely, as u decreases, 1/u increases, so 1/f must increase, and f must decrease. The human eye’s lens changes its shape (accommodation) to adjust its focal length f to focus objects at different distances u onto the fixed retina distance v. The graph in option C shows f increasing as u increases, which is consistent with the lens formula and the process of accommodation.
– For the human eye, the image distance (v) is fixed (distance to the retina).
– The eye lens changes its focal length (f) to focus objects at different distances (u). This process is called accommodation.
– As the object distance (u) increases, the focal length (f) required to focus the image on the retina increases.
– The lens formula is 1/f = 1/v + 1/u. With v constant, f is a function of u.
The graph in option C shows f increasing with u. The functional relationship derived from the lens formula is f(u) = (v*u) / (v+u). The second derivative of this function with respect to u is negative, indicating the curve is concave down, which matches the shape depicted in graph C. Options A and B are incorrect because they show v varying with u, whereas v is constant. Option D shows v varying with f, which is also incorrect as v is constant.

89. A microscope may be a combination of:

A microscope may be a combination of:

[amp_mcq option1=”two convex lenses.” option2=”a convex and a concave lens.” option3=”two concave lenses.” option4=”a convex lens and a convex mirror.” correct=”option1″]

This question was previously asked in
UPSC NDA-1 – 2024
Download PDFAttempt Online
A microscope may be a combination of two convex lenses.
A simple microscope consists of a single convex lens. A compound microscope, which provides higher magnification, typically uses at least two lenses: an objective lens and an eyepiece lens. Both the objective lens and the eyepiece lens in a basic compound microscope setup are convex lenses.
The objective lens (convex) forms a real, inverted, and magnified intermediate image of the object. The eyepiece lens (convex) acts as a simple magnifier, forming a virtual, erect (relative to the intermediate image), and further magnified final image that the observer sees. More complex microscope optics may involve combinations of convex and concave lenses or multiple lens elements to correct aberrations, but the fundamental design of a compound microscope relies on two primary convex lenses.

90. Which of the following is not a part of compound microscope ?

Which of the following is not a part of compound microscope ?

[amp_mcq option1=”Mirror” option2=”Stage” option3=”Clip” option4=”Retina” correct=”option4″]

This question was previously asked in
UPSC NDA-1 – 2024
Download PDFAttempt Online
The correct option is D. The retina is a part of the eye, the organ that perceives the light and forms the image, and is not a component of a compound microscope itself.
A compound microscope is an optical instrument with several components, including the mirror (or light source), stage (for holding the specimen), clips (to hold the slide on the stage), objective lenses, eyepiece, body tube, focus knobs, etc., all working together to magnify an object.
The image formed by the microscope is viewed by the observer through the eyepiece, and this image is ultimately focused onto the retina of the observer’s eye. While the retina is crucial for seeing the magnified image, it is functionally distinct from the microscope’s structure.
Page 1Page 2Page 3Page 4Page 5